year 3 maths's programme, term 1

Developed by L. Williamson, 2012, revised in 2013 & 2014.

Rationale

All students will develop skills and knowledge in all sub strands of the Mathematics k-6 syllabus (Working Mathematically, Number & Algebra, Measurement &

Geometry and Statistics and Probability). Teaching and learning activities will be designed to enable students to construct understanding for richer learning. A

variety of tasks will be open ended to accommodate the individual differences amongst the students.

Stage

Statement

By the end of Stage 2, students ask questions and use efficient mental and written strategies with increasing fluency to solve problems. They use technology to

investigate mathematical concepts and check their solutions. Students use appropriate terminology to describe and link mathematical ideas, check statements for

accuracy and explain their reasoning.

Students count, order, read and record numbers of up to five digits. They use informal and formal mental and written strategies to solve addition and subtraction

problems. Students use mental strategies to recall multiplication facts up to 10 × 10 and related division facts. They use informal written strategies for

multiplication and division of two-digit numbers by one-digit numbers. Students represent, model and compare commonly used fractions, and model, compare and

represent decimals of up to two decimal places. Students perform simple calculations with money and solve simple purchasing problems. They record, describe and

complete number patterns and determine missing numbers in number sentences. Students recognise the properties of odd and even numbers.

Students estimate, measure, compare, convert and record length, area, volume, capacity and mass using formal units. They read and record time in hours and

minutes, convert between units of time, and solve simple problems involving the duration of time. Students name, describe and sketch particular three-dimensional

objects and two-dimensional shapes. They combine and split two-dimensional shapes to create other shapes. They compare angles using informal means and

classify angles according to their size. Students use a grid-reference system to describe position, and compass points to give and follow directions. They make

simple calculations using scales on maps and plans.

Students collect and organise data, and create and interpret tables and picture and column graphs. They list all possible outcomes of everyday events, and

describe and compare chance events in social and experimental contexts.

Objectives

Knowledge, Skills and Understanding

Students:

Working Mathematically

•develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills

and mathematical techniques, communication and reasoning

Number and Algebra

•develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation

Measurement and Geometry

•identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying


formulas, strategies and geometric reasoning in the solution of problems

Statistics and Probability

•collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements.

Values and Attitudes

Students:

•appreciate mathematics as an essential and relevant part of life, recognising that its cross-cultural development has been largely in response to human needs

•demonstrate interest, enjoyment and confidence in the pursuit and application of mathematical knowledge, skills and understanding to solve everyday problems

•develop and demonstrate perseverance in undertaking mathematical challenges.

Organisation

The Maths program will run five days a week for one hour and half hours per day. The program will incorporate explicit teaching using hands-on resources for

active learning and student engagement. Games and / or drills will be incorporated daily to develop basic skills and facts, and to promote automaticity. Each lesson

will be planned to include the four explicit learning phases:

Orientation: This will focus, motivate and assess students’ prior knowledge> it is also an opportunity for revision of skills through games/drills to develop

automaticity.

Guided Discovery: Explicit teaching occurs to introduce a new concept, skill or understanding.

Exploration: These activities will allow students to construct their own understanding of the concept. They may be undertaken individually, in pairs, small groups

or as a whole class. In some lessons groups will comprise students of different skill development levels to provide opportunities from peer learning. The

exploration phase is an optimum time for assessment of learning.

Reflection: The teacher consolidates lesson concepts and skills. Learners will share/explain/justify their learning and the teacher will challenge and extend their

learning. Learners and teachers can reflect on the content of the lesson and on their own learning (cognition) in the lesson through three focus areas: factual

(what did I learn?), strategic (how did I learn?) and application ( and now what will I do with this knowledge?).

Revision/mentals

It is important that students have opportunities to practise and consolidate their knowledge in order to retain new concepts

and skills. This will be achieved through daily number drills, daily work on various aspects of the numeracy continuum (

notebook file), revision of the four operations on a weekly basis and mentals. Mentals will be incorporated at the beginning of

four lessons per week after the number drill practise. This will consist of:

1 day – Naplan style questions

1 day – problem solving type questions

1 day – Number facts

1 day- Mixed mentals across all strands to consolidate covered content

Demonstration

Each new concept will be explicitly taught through several strategies that involve teacher demonstration and explanation as to

the role of the mathematical component. The strategies include:

- explicit teaching of mathematical language.

- chalk and talk,

- use of concrete materials,

- role play,

- problem solving,


- student involvement in demonstrations.

Teacher directed During student practice of strategies and completion of activities, it is important to direct student learning by guiding them

through tasks. This will lay a firm foundation for independent learning.

Independent It is imperative that students learn to complete tasks with confidence and independence. This will also communicate student

development and level of understanding and skill.

Marking To involve students in their work and encourage immediate reteaching of any misconceptions, when possible students need to

be involved in the marking of their work by either marking some their work, having a peer mark work , watch the teacher mark

work and discuss mistakes or review marked work from the previous lesson.

Outcomes and activities will be included on a daily weekly basis. Below is a list of experiences which will be included on a daily basis prior to mentals activities. Will

form as part of the number drill component:

Monday Tuesday Wednesday Thursday Friday

Counting forwards and

backwards by tens or

hundreds on and off the

decade

Placing a set of three-

and four-digit numbers in

ascending or descending

order. (Continuum

Notebook File)

Reciting timetables

Recording three- and

four-digit numbers using

expanded notation e.g.

5429 = 5000 + 400 + 20 + 9

(Continuum Notebook File)

Reading numerals to

9999 and stating the

place value of units,

tens, hundreds &

thousands using number

flip chart

Reciting Timetables

Identifying the number

before and the number

after a given two, three

or four-digit number


Reading numbers on an

abacus

Reciting Timetables

Revise mathematical

language relating to

concept for the week.

Writing numerals as

words (Continuum

Notebook File)

Reciting timetables

Using the symbols for ‘is

less than’ (<) and ‘is

greater than’ (>) to show

the relationship between

two numbers.


Reciting timetables

Yearly Overview

Term 1 Term 2 Term 3 Term 4

Whole Numbers (TENS)

Multiplication & Division (TENS)

Fractions

Data

Volume & Capacity

3D shapes

Patterns & Algebra (TENS)


Addition & Subtraction (TENS)

Position

Time

Length

2D Shapes


Multiplication & Division (TENS)

Patterns & Algebra (TENS)

Chance

Angles

Data

Area


Addition & Subtraction (TENS)

Fractions & Decimals

Mass

2D shapes

Length


Aboriginal and

Torres Strait

Islander

Perspectives

Mathematics provides opportunities for students to strengthen their appreciation and understanding of Aboriginal peoples and Torres Strait Islander peoples and

their living cultures. Specific content and skills within relevant sections of the curriculum can be drawn upon to encourage engagement with:

•Aboriginal and Torres Strait Islander frameworks of knowing and ways of learning

•Social, historical and cultural contexts associated with different uses of mathematical concepts in Australian Indigenous societies

•Aboriginal peoples’ and Torres Strait Islander peoples’ contributions to Australian society and cultures.

Mathematics provides opportunities to explore aspects of Australian Indigenous knowing in connection to, and with guidance from, the communities who own them.

Using a respectful inquiry approach students have the opportunity to explore mathematical concepts in Aboriginal and Torres Strait Islander lifestyles including

knowledge of number, space, measurement and time. Through these experiences, students have opportunities to learn that Aboriginal peoples and Torres Strait

Islander peoples have sophisticated applications of mathematical concepts which may be applied in other peoples’ ways of knowing.

General capabilities

and cross-curriculum

priorities

Opportunities to engage with:




Key to general

capabilities and

cross-curriculum

priorities

Literacy Numeracy ICT capability Critical and creative thinking Ethical behaviour Personal and social capability Intercultural understanding

Aboriginal and Torres Strait Islander histories and cultures Asia and Australia’s engagement with Asia Sustainability

Quality Teaching

QUALITY LEARNING ENVIRONMENT

Substantive communication

What activities and groupings will encourage and

maintain communication across and within the

class groups?

Are students using talk to learn?

Social support

What support needs to be modelled / scaffolded

and encouraged so that all students learn, take

risks and participate?

Engagement

Which activities that relates to the focus will

meaningfully engage all students?

Student self-regulation

Do the activities allow for students to be on task

for all / most of the lesson?

Intellectual Quality

Deep knowledge

What do I know about the unit / focus?

What deep knowledge forms the basis of these

activities?

What deep knowledge do students need to develop?

What deep knowledge do I explicitly need to teach?

Problematic knowledge

Can aspects of deep knowledge be seen from

different points of view?

Are opinions being explored and not just stated?

Whose viewpoints are missing?

Do the resources present a particular viewpoint?

Metalanguage

What metalanguage (technical, topic related

language) will be discussed, used, talked about and

explained?

Significance

Background knowledge

What background knowledge / experiences from

outside school and previous lessons can be drawn on to

introduce / link / reinforce focus?


Connectedness

Have connections been made to real life purposes?

Have the connections been made clear to students?

Assessment

Assessment Tasks will be part of the maths program and these will be used for reports at half-yearly and yearly intervals.

Useful websites

for all strands.

http://www.amathsdictionaryforkids.com/dictionary.html - A maths dictionary

http://www.amathsdictionaryforkids.com/mathsCharts.html - Numerous Printable Maths Charts for all strands

http://www.studyladder.com.au/?lc_set

Other useful websites related to particular strands are posted at the end of each week and throughout the

program if relevant to specific lessons

http://www.amathsdictionaryforkids.com/dictionary.html

http://www.amathsdictionaryforkids.com/mathsCharts.html

http://www.studyladder.com.au/?lc_set


Stage 2 Checklist of Outcomes and Content Descriptors

Stage 2 Numbers and Algebra T1 T2 T3 T4

Whole Numbers

Applies place value to order, read and represent numbers of up to five digits (MA2-4NA)

Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) x x x x Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) x x x x Recognise, represent and order numbers to at least tens of thousands (ACMNA072) x x x x Addition and Subtraction

Uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers (MA2-5NA)

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

(ACMNA055) x x x x

Recognise and explain the connection between addition and subtraction (ACMNA054) x x Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

(ACMNA059) x x

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve

problems (ACMNA073) x x

solve problems involving purchases and the calculation of change to the nearest five cents, with and without the use of digital technologies (ACMNA080) x x Multiplication and Division

Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation (MA2-6NA)

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) x x

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies

(ACMNA057) x x

Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075) x x x x

http://syllabus.bos.nsw.edu.au/glossary/mat/partitioning/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/place-value/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/partitioning/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/multiplication/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/multiplication/?ajax


Stage 2 Measurement and Geometry T1 T2 T3 T4

Length

Develop efficient mental and written strategies, and use appropriate digital technologies, for multiplication and for division where there is no

remainder(ACMNA076) x x

Use mental strategies and informal recording methods for division with remainders. x x

Fractions and Decimals Represents, models and compares commonly used fractions and decimals (MA2-7NA)

Model and represent unit fractions, including halves, quarters, thirds and fifths and their multiples, to a complete whole

(ACMNA058) x

Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number

line(ACMNA078) x

Investigate equivalent fractions used in contexts (ACMNA077) x Recognise that the place value system can be extended to tenths and hundredths, and make connections between fractions and decimal

notation (ACMNA079) x Patterns and Algebra Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by

calculating missing values (MA2-8NA)

Describe, continue and create number patterns resulting from performing addition or subtraction (ACMNA060) x Investigate the conditions required for a number to be even or odd and identify even and odd numbers (ACMNA051)

x

Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083) x Investigate and use the properties of even and odd numbers (ACMNA071) x Investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9 (ACMNA074) x Explore and describe number patterns resulting from performing multiplication (ACMNA081) x Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082) x

http://syllabus.bos.nsw.edu.au/glossary/mat/remainder/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/unit-fraction/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/multiple/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/numeral/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/number-line/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/number-line/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/equivalent-fractions/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/place-value/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/decimal/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/even-number/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/odd-number/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/even-number/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/odd-number/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/multiple/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/remainder/?ajax


Measure, order and compare objects using familiar metric units of length (ACMMG061) x

Use scaled instruments to measure and compare lengths (ACMMG084) x

Use scaled instruments to measure and compare temperatures (ACMMG084) x

Area

Measures, records, compares and estimates areas using square centimetres and square metres (MA2-10MG)

Recognise and use formal units to measure and estimate the areas of rectangles x

Compare the areas of regular and irregular shapes by informal means (ACMMG087) x Compare objects using familiar metric units of area (ACMMG290) x Volume and Capacity

Measures, records, compares and estimates volumes and capacities using litres, millilitres and cubic centimetres (MA2-11MG)

Measure, order and compare objects using familiar metric units of capacity (ACMMG061) x Compare objects using familiar metric units of volume (ACMMG290) x Use scaled instruments to measure and compare capacities(ACMMG084) x Mass

Measures, records, compares and estimates the masses of objects using kilograms and grams (MA2-12MG)

Measure, order and compare objects using familiar metric units of mass (ACMMG061) x Use scaled instruments to measure and compare masses (ACMMG084) x Time

Reads and records time in one-minute intervals and converts between hours, minutes and seconds (MA2-13MG)

Tell time to the minute and investigate the relationship between units of time (ACMMG062) x

http://syllabus.bos.nsw.edu.au/glossary/mat/rectangle/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/irregular-shape/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/capacity/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/capacity/?ajax


Convert between units of time (ACMMG085) x

Use am and pm notation and solve simple time problems (ACMMG086) x

Read and interpret simple timetables, timelines and calendars x

3D Space Makes, compares, sketches and names three-dimensional objects, including prisms, pyramids, cylinders, cones and spheres, and describes their features (MA2-14MG)

Make models of three-dimensional objects and describe key features (ACMMG063) x

Investigate and represent three-dimensional objects using drawings x

2D Space Manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features (MA2-15MG) Compare and describe features of two-dimensional shapes, including the special quadrilaterals

x Identify symmetry in the environment (ACMMG066) x Compare and describe two-dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088) x Create symmetrical patterns, pictures and shapes, with and without the use of digital technologies (ACMMG091)

x Angles

Identifies, describes, compares and classifies angles (MA2-16MG)

Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) x

Compare angles and classify them as equal to, greater than or less than a right angle(ACMMG089) x

Position

Uses simple maps and grids to represent position and follow routes, including using compass directions (MA2-17MG) Create and interpret simple grid maps to show position and pathways (ACMMG065) x Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) x Stage 2 Statistics and Probability T1 T2 T3 T4

http://syllabus.bos.nsw.edu.au/glossary/mat/line-symmetry/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/angle/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/angle-classification/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/angle/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/right-angle/?ajax


Data

Selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs (MA2-18MG)

Identify questions or issues for categorical variables; identify data sources and plan methods of data collection and recording

(ACMSP068) x Collect data, organise it into categories, and create displays using lists, tables, picture graphs and simple column graphs, with and without the

use of digital technologies (ACMSP069) x Interpret and compare data displays(ACMSP070) x Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095) x Construct suitable data displays, with and without the use of digital technologies, from given or collected data; include tables, column graphs

and picture graphs where one picture can represent many data values (ACMSP096) x Evaluate the effectiveness of different displays in illustrating data features, including variability (ACMSP097)

x Chance

Describes and compares chance events in social and experimental contexts (MA2-19MG)

Conduct chance experiments, identify and describe possible outcomes, and recognise variation in results (ACMSP067) x

Describe possible everyday events and order their chances of occurring (ACMSP092) x

Identify everyday events where one occurring cannot happen if the other happens (ACMSP093) x

Identify events where the chance of one occurring will not be affected by the occurrence of the other (ACMSP094) x

Stage 2 Working Mathematically T1 T2 T3 T4

Uses appropriate terminology to describe, and symbols to represent, mathematical ideas (MA2-1WM) x x x x Selects and uses appropriate mental or written strategies, or technology, to solve problems (MA2-2WM) x x x x Checks the accuracy of a statement and explains the reasoning used (MA2-3WM) x x x x

http://syllabus.bos.nsw.edu.au/glossary/mat/categorical-variable/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/data/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/picture-graphs/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/column-graph/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/data-display/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/data/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/data-display/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/column-graph/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/picture-graphs/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/probability/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/event/?ajax

http://syllabus.bos.nsw.edu.au/glossary/mat/probability/?ajax


Week Monday Tuesday Wednesday Thursday

2

Addition facts to 20

Example:

7 + 4 =

11 + 8 =

+ 7= 20

3 + = 20

Adjustment: Reduce/extend the number

facts based on TEN ability

1. Lucy went to the grocery store.

She bought 9 packs of cookies and

7 packs of noodles. How many packs

of groceries did she buy in all?

2. Roden went to a pet shop. He

bought 5 gold fish and 7 blue fish.

How many fish did he buy?

3. I read 21 pages of my English

book yesterday. Today, I read 17

pages. What is the total number of

pages did I read?

Subtraction facts to 20

Example:

7 - 4 =

11 - 8 =

- 7= 20

23 + = 20



3

Number Patterns (skip counting)

Example:

Complete the following:

5, 10, 15, 20, __, __, __, __, __

2, 4, 6, 8, __, __, __, __, __

10, 20, 30, 40, __, __, __, __, __

1. Jose has 8 chickens and 8 ducks.

How many fowls does he have?

2. Gino has 13 popsicle sticks. I

have 8 popsicle sticks. What is the

sum of our popsicle sticks?

3. Lino picked up 19 shells on the

seashore in the morning and 7 shells

Addition and subtraction facts to

20

Example:

17 - 4 =

11 + 8 =

+ 7= 20


Adjustment: 100s chart to assist skip

counting may be required by some students.

in the afternoon. How many shells

did he pick up in all?

27 - = 20




Outcomes & Indicators:

Term 1

Weeks 1 -3

Number & Algebra

Whole Numbers 1 NSW Curriculum

Outcomes & Indicators A student:

MA2-1WM:uses appropriate terminology to describe, and symbols to represent, mathematical

ideas

MA2-2WM: selects and uses appropriate mental or written strategies, or technology, to solve

problems

MA2-3WM:checks the accuracy of a statement and explains the reasoning used

MA2-4NA: applies place value to order, read and represent numbers of up to five digits

Australian Curriculum Outcomes & Indicators

ACMNA052

Recognises , models , represents and orders four digit numbers

Reproduces numbers in words using their numerical representations and vice a versa

Identifies the number before and after a given four digit number

Uses the symbol for ‘is less than’ (<) and is greater than’’ (>) to show the relationship

between two four digit numbers.

Counts forwards and backwards by tens or hundreds, on and off the decade

Uses four digit numbers

Language

Students should be able to communicate using the following language: number before, number after, more than, greater than, less than, largest number, smallest number, ascending order,

descending order, digit, zero, ones, groups of ten, tens, groups of one hundred, hundreds, groups of one thousand, thousands, place value, round to. The word 'and' is used between the

hundreds and the tens when reading and writing a number in words, but not in other places, eg 3568 is read as 'three thousand, five hundred and sixtyeight'. The word 'round' has

different meanings in different contexts, eg 'The plate is round', 'Round 23 to the nearest ten'. .


Background Information

The place value of digits in various numerals should be investigated. Students should understand, for example, that the '5' in 35 represents 5 ones, but the '5' in 53 represents 50 or 5

tens.

Teaching and Learning

Recite 2 & 10 times tables

Resources

PRETEST: Number & Algebra Strand (will be used to form ability groups, as well as place students in their cluster levels on

the Numeracy Continuum)

Assessment

Task

Lesson 1

Date:

Focus: Write and model two, three & four digit numbers

O Choose one student to be “it”. Display a three digit number for the class to see (but not the chosen student). The chosen student calls out a three

digit number and the class responds with the words higher or lower until the number is guessed

G Students work in small groups to model given 2, 3, & 4 digit numbers ( based on TEN ability) with MAB base 10 material, for example make the

number 263, 170, 308 and so on.

E Students practice making numbers with MAB and record the number made on individual whiteboards. Have students after they have made three or

four numbers circle the number which is the largest and cross which is the smallest and say how they know.

Worksheet: Primary Mathematics Book D page 45 (differentiated worksheet depending on ability)

R Count as a class forwards or backwards from a given three or four digit number.

Adjustment: Reduce/extend the number of digits

-MAB Base 10

material

-white boards

and markers

- worksheet

Primary

Mathematics

Book D page

45

Lesson 2

Date:

Focus: Write, model and order three & four digit numbers Language Focus: before and after

O Go to the website below and select the second level to have students order three and four digit numbers.

http://www.bbc.co.uk/schools/ks1bitesize/numeracy/ordering/index.shtml

G Ask students to write a number between 100 and 1000 on their white board. Write a three digit number on the board (for example 375) and ask any

student whose number is larger to stand up and say their number. Continue in this way for numbers that are larger or smaller than a number you write on

the board.

E Play number before and after with 3/4 deck of cards (number of cards based on TEN ability) Take a number from each deck of cards to make a

number, students are to say the number that comes before and after the made number and record in their work book by ruling three columns.

-website

-whiteboards

and markers

-playing cards

& workbooks

http://www.bbc.co.uk/schools/ks1bitesize/numeracy/ordering/index.shtml


before number made after

R Share results with friends. Discuss strategies used. Count as a class forwards or backwards from a given three digit number.


Lesson 3

Date:

Focus: Write, model and order three & four digit numbers Language Focus: ascending and descending

O Play HIGHER OR LOWER

Two players and adjudicator are selected from the class. The teacher gives the adjudicator a card upon which is written a number. Initially the numbers

given could be three-digit numbers. Later they could be four-digit numbers. The players are told outer bounds for the number on the card, eg “The

number is between 4 000 and 5 000.” The first player makes a guess and the adjudicator responds by telling the players whether the number is higher or

lower than the one guessed. The other player then offers a number and the adjudicator responds. The game continues until a player gives the correct

number. Discuss the strategies used by players.

G Collect some of the number cards that the students wrote on in the game above, mix them up and give to some of the students. Have the students

stand up in front of the class and put themselves in order from smallest to largest.

Reinforce the 'think aloud' strategy to show how to order three and four digit numbers from smallest to largest. Thinking aloud to order four-digit

numbers (2253, 1233, 4223, 1223)

The teacher models the 'think aloud' strategy to show how to order these numbers. Say, I read each number and ask which is the biggest? I will look at

the thousands digit first. The number with four thousands is the biggest. I will put 4223 last on the number line.

There are two numbers with one thousand so I must look at the hundreds in these numbers. Both numbers have two hundreds so I must look at

the tens. One number has three tens and one number has two tens. The number with three tens is bigger than the number with two tens. 1233 is

bigger than 1223. 1223 is the smallest number so I will put it first on the number line.

1233 is next and is very close to 1223. I will put 1233 close to 1223 on the number line.

Now I have one number left, 2253. 2253 comes after 1233 and before 4223. If I look at the thousands digit I can see that two thousand is

closer to one thousand than to four thousand so I will put 2253 closer to 1233 than to 4223.

-blank card

-worksheet

p43 Primary

Mathematics

Book D


E Worksheet: p43 Primary Mathematics Book D (differentiated worksheet depending on ability)

R Share results with friends. Discuss strategies used. Place random numbers on the floor and select students to place the numbers in order from

smallest to largest and vice a versa.


Lesson 4

Date:

Focus: Expand and compare three digit numbers. Language Focus: smallest, largest, forwards and backwards O Discuss the place value of individual digits within numbers. Compare the different place value of the same digit in different numbers (for example

compare the value of 9 in the numbers 49 and 192). Ask students to make both of these numbers using MAB materials and compare the differences.

Repeat for other pairs of numbers.

G Model different ways to write 3 and four digit numbers on the board in the following table.

Number Place Value In words MAB Picture

132 100+30+2 1 hundred, 3 tens, 2 units

or One hundred and thirty two.

E Students complete worksheet and use MAB to model numbers.

Worksheet: p46 Primary Mathematics Book D (differentiated worksheet depending on ability)

R Share findings and discuss any numbers that may have caused problems, eg use of zero.

-MAB

material

-worksheets

p46 Primary

Mathematics

Book D

Lesson 5

Date:

Focus: Write, model and order three digit numbers

O In small groups, students use a pack of playing cards with the tens and picture cards removed. The Aces are retained and count as 1. The Jokers are

retained and count as 0. Student A turns over the first 3 cards and each player makes a different three-digit number. Student A records the numbers

and puts the cards at the bottom of the pile. Students each take a turn in turning over three cards and recording the group's three-digit numbers. When

each student has had a turn they sort and order their numbers. Students extend the game by making four-digit numbers.

Possible questions include:

Can you read each number aloud?

Can you order the numbers in ascending and descending order?

Can you state the place value of each numeral?

What is the largest/smallest number you can make using three cards/four cards?

What is the next largest/smallest number you can make using three cards/four cards?

Can you identify the number before/after one of your three digit/four-digit numbers?

Can you find a pattern? How can you describe your pattern? How can you continue the pattern?

How many different ways can you represent each number? (expanded notation, in words)

-decks of

playing cards

-worksheets

p42 Primary

Mathematics

Book D


Can you count forwards/backwards by tens/hundreds from one of your three-digit/four-digit numbers?

Can you round one of your three-digit or four-digit numbers to the nearest hundred? to the nearest thousand?

E Worksheet: p42 Primary Mathematics Book D (differentiated worksheet depending on ability)

R Place random numbers on the floor and select students to place the numbers in order from smallest to largest and vice a versa.


Lesson 6

Date:

Focus: Write, model and order three & four digit numbers) Language Focus: more than, less than

O Play Count n Catch – Students, in pairs, sit or stand about one metre away from each other, one with a ball or bean bag in their hand. The teacher calls

out the first number in the skip counting pattern. The student with the ball calls out the next number as they toss the ball to their partner. How far can

the count to in one minute?

Variation: Start at a higher number and count backwards. Can they reach zero before one minute is up?

G Show students card 9 from the Maths in a Box level 2. Ask them to make the number 9747 using Base 10 materials. Discuss the place value

(thousands, hundreds, tens and ones). Ask:

What is one more than 9747?

What is one less than 9747?

What is ten more than 9747?

What is ten less than 9747?

What is 100 more than 9747?

What is 100 less than 9747?

What is 1000 more than 9747?

What is 1000 less than 9747?

E Students work in pairs and roll four dice, one representing thousands, hundreds, tens & ones and record their four digit number. They then work

together to complete the following table.

Four digit

number

1 more 1 less 10 more `10 less 100 more 100 less 100 more

R Share results with friends. Discuss strategies used. Count as a class forwards or backwards from a given three or four digit number.


Card 9 (Maths

in a box level

2)

thousands,

hundreds,

tens & ones

dice


Lesson 7

Date:

Focus: Write and order four digit numbers Language Focus: hundreds, tens, ones, thousands, place value, more than, less than, greater than,

smaller than

O In pairs, students are given three different-coloured dice, representing hundreds, tens and ones. Students take turns to throw the dice, record their

three-digit number and state the number before and after..

G & E Introduce and discuss the symbols we use for comparing numbers.

Using individual whiteboards have students record to numbers and discuss which symbol will be used.

Work sheet (optional): P 5 & 6 Mathletics Whole numbers Book D (differentiated worksheet depending on ability)

R Revise all the ways that four digit numbers can be written or represented. Ensure that students can link all of the matching representations. Play

games such as concentration to encourage students to recall the representations and recall positions of particular cards.


Whiteboards

& Markers

Work sheet

(optional):

P 5 & 6

Mathletics

Whole

numbers Book

D

Focus: Model and expand four digit numbers Language Focus: hundreds, tens, ones, thousands, place value

O Using MAB material as support, ask students to count by 100’s: 100, 200, 300…..800, 900. Discuss what happens when the next 100 is added? (we

reach 1000). Record the number name along with the number on the board. Use the class value chart to explain the progression of places (ones, tens,

hundreds and then thousands)

MAB Blocks


Lesson 8

Date: G Take the stack of 10 hundreds blocks and compare it with the single thousands block. Make the exchange and continue the counting by hundreds: 1100,

1200, 1300…..and so on, until 1900 is reached. Discuss with the students that another exchange will need to take place after the next block is added.

Students can make the exchange and say the new number. (Two Thousand). Write some four digit numbers on the board. Ask some students to read the

numbers aloud. Choose some students to represent the numbers with MAB. Give students a copy of BLM 18 (Numeral expanders) and after they have cut

out the numeral expanders show them how to record numbers in each space and fold the expander to make a four digit number. Ask them to write some

of their four digit numbers in expanded form (that is 1693 =1000 + 600 + 90 + 3). Ask students to write a four digit number on a small piece of paper and

then stand in a circle. Give instructions, such as: if your number is more than 8000, sit down, if you have a number with 500 hundreds sit down. Continue

until one student is left standing. Ask that student to read out their number.

E Activity: Have students roll a thousands, hundreds, Tens & ones dice and record in work book as numeral and the matching expanded notation

R Ask students to count large numbers, in the thousands. Say a number to the class then ask one student to say the number before and another to say

the number after. Discuss the strategies the students used to do this.


Dice

(thousands,

hundreds,

tens & ones)

Lesson 9

Date

Assessment task: Whole Number

Useful Websites:

http://www.superteacherworksheets.com/place-value.html

http://pbskids.org/cyberchase/games/negativenumbers/negativenumbers.html

http://www.topmarks.co.uk/Interactive.aspx?cat=21

Were the activities engaging? Yes/No

Were the activities purposeful? Yes/No

Can the students order three digit numbers? Yes/ No

Which students need to consolidate their understanding?

http://www.superteacherworksheets.com/place-value.html

http://pbskids.org/cyberchase/games/negativenumbers/negativenumbers.html

http://www.topmarks.co.uk/Interactive.aspx?cat=21


Evaluation

&

Assessment

Have my students been able to transfer their learning from practical

experiences to independent work? Yes/No

Can students model and recognise models of three digit numbers? Yes/No

Can students represent three digit numbers in expanded notation? Yes/NO


Can the students order three & four digit numbers? Yes/ No


Can students model and recognise models of three & four digit numbers? Yes/No

Can students represent three & four digit numbers in expanded notation? Yes/NO


Which students require remediation?

Which students require extension work?

Other comments:



4


30

Example:

37 - 9 =

19 + 8 =

+ 7= 30

38 - = 30



1. There were 11 parents in the

program and 17 pupils, too. How

many people were present in the

program?

2. Last Saturday, Marie sold 25

magazines and 8 newspapers. What

is the total number of reading

materials she sold?

3. There are twelve (12) birds on

the fence. Eight (8) more birds land

on the fence. How many birds are on

the fence?


Example:


95, 90, 85, 80, __, __, __, __, __

12, 14, 16, 18, __, __, __, __, __

10, 20, 30, 40, __, __, __, __, __




Example:

1. Twenty-two (22) boys went down

the slide. Thirteen (13) more boys

went down the slide. How many boys

Recording three- and four-digit

numbers using expanded notation

e.g. 5429 = 5000 + 400 + 20 + 9


5


5, 10, 15, 20, __, __, __, __, __

2, 4, 6, 8, __, __, __, __, __

10, 20, 30, 40, __, __, __, __, __



went down the slide?

2. Thirteen (13) ducks are

swimming in a lake. Twenty (20)

more ducks come to join them. How

many ducks are swimming in the

lake?

3. Thirty (30) dogs are barking. Ten

(10) more dogs start to bark. How

many dogs are barking?





Term 1

Weeks 4 /5

Number & Algebra

Multiplication & Division

NSW Curriculum Outcomes & Indicators

A student:

MA2-1WM: uses appropriate terminology to describe, and symbols to represent,

mathematical ideas

MA2-2WM: selects and uses appropriate mental or written strategies, or technology,

to solve problems

MA2-3WM: checks the accuracy of a statement and explains the reasoning used

MA2-6NA: uses mental and informal written strategies for multiplication and division


ACMNA057

Links multiplication and division facts using groups on arrays

Language:

Students should be able to communicate using the following language: group, row, column, horizontal, vertical, array, multiply, multiplied by, multiplication, multiplication facts,

double, shared between, divide, divided by, division, equals, strategy, digit, number chart. When beginning to build and read multiplication facts aloud, it is best to use a language pattern of

words that relates back to concrete materials such as arrays. As students become more confident with recalling multiplication facts, they may use less language. For example, 'five rows (or

groups) of three' becomes 'five threes' with the 'rows of' or 'groups of' implied. This then leads to 'one three is three', 'two threes are six', 'three threes are nine', and so on.



In Stage 2, the emphasis in multiplication and division is on students developing mental strategies and using their own (informal) methods for recording their strategies.

Comparing their own method of solution with the methods of other students will lead to the identification of efficient mental and written strategies. One problem may

have several acceptable methods of solution. Students could extend their recall of number facts beyond the multiplication facts to 10 × 10 by also memorising multiples

of numbers such as 11, 12, 15, 20 and 25. An inverse operation is an operation that reverses the effect of the original operation. Addition and subtraction are inverse

operations; multiplication and division are inverse operations. The use of digital technologies includes the use of calculators.


Recite 2, 5 & 10 times tables

Resources

Lesson 1

Date

Focus: Mutiplication (times tables) Language Focus: groups of

O Students brainstorm synonyms for Multiplication ( groups of, rows of, multiply)

Teacher records responses.

Students brainstorm symbols and other words associated with multiplication work.

G Review the idea of multiplication as being groups of groups. Discuss the commutative property in terms of groups of groups, e.g. three groups of 4 will

give the same product as four groups of 3. Show a 3 x 4 array of circles on a card, i.e. three rows with four circles in each row. Rotate this card 90o to

show the same array as 4 x 3, i.e. four rows with three circles in each row.

E View Nelson Teaching Interactive Maths 3 (Unit 14- Groups of) Go through and discuss several examples.

Have students roll two dice. They make the array to match the numbers on the dice: for example if a 3 and a 5 are rolled, the student makes a 3 x 5

array. Have students make up a problem to match their array, for example. There are 3 cars. Each car has 5 passengers. There are 15 passengers

altogether. Provide students with ample time to make numerous arrays to match the numbers rolled on their dice.

R View Notebook File- Multiplication: groups of, and go through with students to ensure their understanding of today’s lesson

Nelson Teaching

Interactive

Maths 3 (Unit

14- Groups of)

Dice

Notebook File-

Multiplication:

groups of

Lesson 2

Date

Focus: Models of the Multiplication Facts

O Ask students to skip count out loud some common counting patterns (for example 2s, 5s and 10s). Have students skip count by 3s and 4s and circle the

number on a hundreds chart

G & E

Part A:Students construct models of the multiplication facts using interlocking cubes. They build a staircase eg with 3 blocks in the first step, 6 in the

second etc, to represent the multiplication facts for 3. Students use a 10 × 10 grid to record their answers.

Part B:Students model the multiplication facts using rectangular arrays and record the associated inverse relationships

eg • • • • 3 × 4 = 12 12 ÷ 3 = 4

• • • • and 4 × 3 = 12 12 ÷ 4 = 3

• • • •

Variation: Students are given a number (eg 12) and asked to represent all its factors using arrays.

interlocking

cubes, grid

paper, paper and

pencils


Adjustment: Pictorial representations on how to create models may be needed

Lesson 3

Date

Focus: Multiplication (times tables) Language Focus: skip counting, arrays



G Show students card 36 from Maths- in a- box (level 2). Ask students to mentally calculate the number of eggs in each carton. Students explain their

strategies. Dis students count by one’s or did they use multiplication strategies?

E Provide students with 12 counters each so they can make an array of coloured eggs. Students circle a group of dots on 1cm square dot paper (BLM 60

Primary maths 3 TRB) to represent this array. Students write two multiplication and two division number sentences for this array.

Students rearrange the 12 counters to make a different array, then circle groups on dots on 1cm dot paper and write two multiplication and two division

number sentences for this array.

R View Notebook File- Multiplication: arrays and go through with students to ensure their understanding of today’s lesson.

Card 36 from

Maths- in a- box

(level 2).

Counters

BLM 60 Primary

maths 3 TRB

Notebook File-

Multiplication:

arrays

Lesson 4

Date

Focus Multiplication

O Number Problems Teacher poses a variety of number problems to the students that require the application of multiplication skills e.g 20 biscuits, 30

oranges or 40 tennis balls or If you had ____ chairs with _____ cats/dogs/babies on each chair how many cats/dogs/babies would you have altogether?

Students;

Are able to use a variety of materials to solve their problem.

Record using visuals, how they solved the problem.

G Paddle pop sticks in Cups

In pairs, students place five cups on a table and put an equal amount of paddle pop sticks in each cup.

Students respond to the following questions;

o How many cups are there?

o How many paddle pop sticks are in each cup?

o How many paddle pop sticks did you use altogether?

o How did you work out the answer? (you cannot start from 1 and count each)

Students share their strategies with the class.

Students record their strategy using numerals, symbols or words.

E Worksheet: Primary Mathematics Book B, C & D (differentiate sheet according to students ability level)

Paddle pop

sticks, cups

worksheets

: Primary

Mathematics

Book B, C & D


R Share strategies and finish with a game of Buzz using multiplies of 5 & 10.

Lesson 5

Date

Focus: Multiplication (times tables) Language Focus: skip counting, arrays



G Remind students that arrays show groups of or rows of and these can be linked to multiplication facts. For example, an array that shows 5 groups of 3

can be linked to the multiplication fact. Use counters to make arrays for some 3 and 4 times tables.

E Worksheet: p 59 & 60 Primary Mathematics Book D

R Recite 3 and 4 times tables.

hundreds chart

Worksheet:

p 59 & 60

Primary

Mathematics

Book D

Lesson 6

Date

Focus: Relate the twos and four times tables Language Focus: skip counting, arrays

O Recite two and four times tables.

G & E Ask students to complete the first activity on student book page 35 (activity 3, Maths Plus 3 Student Work Booklet). Ask: what do you notice

about the answers to the 2 times and 4 times tables? (The 4 times answers are double the answers for the 2 times tables) Why is this? Discuss.

Write 8 x 2 on the board and establish that the answer is 16. Ask students to describe how they can use this fact (8x2=16) to work out 8 x 4. Repeat

for other times table facts.

Say to students: if we know that 2 times tables are worked out by doubling, for example 3 x 2 is double 3, and that the 4 times tables are double the 2

times tables, then this is two lots of doubling (double 3 is 6 and double 6 is 12) so to work out the answers to 4 times tables, we should be able to double

and then double again. Work through the 4 times tables as a class, using this strategy ( for example, for 8 x 4, double 8 is 16 and double 16 is 32, so 8 x

4 = 32

Worksheet page 9 & 10 Mathletics Multiplication & Division student work booklet D

R Recite 2 and 4 times tables.

Worksheet:

page 35 Maths

Plus 3 Student

Work Booklet)

Worksheet

page 9 & 10

Mathletics

Multiplication &

Division student

work booklet D

Optional /

Additional

learning

experiences

1. Tables Races

Students make up cards for particular multiplication facts for particular numbers, shuffle them and put them into an envelope eg

cards,

pencils, paper, envelopes


In groups, students are given an envelope of cards. Students race each other to put the cards into order, skip counting aloud. Students state which

number has the multiplication facts their cards represent.

Variation: Students write numbers in descending order.

Adjustment: 100s chart to assist skip counting may be required by some students. Extend the number of cards used or remove a card so missing card

has to be identified

2. Multiplication Grid

Students keep a multiplication grid, as shown. When students are sure they have learnt particular multiplication facts, they fill in that section of the

grid. Students are encouraged to recognise that if they know 3 × 8 = 24 they also know 8 × 3 = 24, and so they can fill in two squares on the grid.

multiplication

grid, pencils

Lesson 7

Date

Assessment task: Multiplication

Please Note:

Times tables will be drilled/ recited daily throughout the whole year. There are a number of interactive games that can be played to assist with keeping

the students engaged. Some include:

http://www.lightningeducation.com/timestables.html Random Times tables

http://www.lightningeducation.com/missingtimestables.html missing addends times tables

http://www.lightningeducation.com/timestables.html

http://www.lightningeducation.com/missingtimestables.html



6



e.g. 5429 = 5000 + 400 + 20 + 9



1. Bobby ate twenty-six (16) pieces

of candy. Then, he ate seventeen

(17) more. How many pieces of

candy did Bobby eat?

2. Sandy had twenty-six (26) pet

fish. She bought six (6) more fish.

How many pet fish does Sandy have

now?

3. Tessa has 4 apples. Anita gave

her 5 more. She needs 10 apples to

make a pie. Does she have enough to

make a pie?


30

Example:

35 - 8 =

9 + 18 =

+ 13= 30

42 - = 30



7

Repeated addition and

multiplication fact

Example:

2 + 2 + 2 + 2 =

1. Julia played tag with 12 kids on

Monday. She played tag with 7 kids

on Tuesday. How many kids did she

play with altogether?

2. Molly had 9 candles on her

birthday cake. She grew older and

Have students write stories and

number sentences for the

numbers 10, 12 and 16

Example:

2 x5 = 10 20 - 10=10


4 lots of 2 +

4 x 2 =

Adjustment: 100s charts to assist skip

counting and counters to make groups of may

be required by some students.

got 6 more on her birthday cake.

How old is Bailey now?

3. James ate 9 cookies before

dinner and 7 cookies after dinner.

How many cookies did he eat?

1 + 9 =10 40 ÷ 4 = 10

John had 7 marbles and Susie gave

him three. He now has 10 marbles.






Term 1

Weeks 5 / 6


Three Dimensional Shapes 1


A student:


mathematical ideas


MA2-14MG: makes, compares, sketches and names three-dimensional objects,

including prisms, pyramids, cylinders, cones and spheres, and describes their

features


ACMMG063

compares and describes features of prisms, pyramids, cylinders, cones & spheres

Identifies and names three dimensional objects as prisms, pyramids, cylinders, cones and

spheres

Recognises similarities and differences between prisms, pyramids, cylinders, cones and

spheres

Language:

Students should be able to communicate using the following language: object, two-dimensional shape (2D shape), three-dimensional object (3D object), cone, cube,

cylinder, prism, pyramid, sphere, surface, flat surface, curved surface, face, edge, vertex (vertices), net. In geometry, the term 'face' refers to a flat surface with only


straight edges, as in prisms and pyramids, eg a cube has six faces. Curved surfaces, such as those found in cylinders, cones and spheres, are not classified as 'faces'.

Similarly, flat surfaces with curved boundaries, such as the circular surfaces of cylinders and cones, are not 'faces'. The term 'shape' refers to a two-dimensional

figure. The term 'object' refers to a three dimensional figure.


The formal names for particular prisms and pyramids are not introduced in Stage 2. Prisms and pyramids are to be treated as classes for the grouping of all prisms and

all pyramids. Names for particular prisms and pyramids are introduced in Stage 3.


Recite 3, & 4 times tables

Resources

Lesson 1

Date

Focus: Name, sort and describe 3D shapes Language Focus: cones, cylinders, prisms, spheres, properties, faces, edges and corners

O Have students counting forwards and backwards by tens or hundreds on and off the decade. Then introduce the topic by sharing the following

website:

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm

G Divide the class into small groups. Give each group a 3D shape to explore. Ask each group to draw the shape, list its properties, give an example of it

and draw a model of it. Include the whole class in a discussion about the information the groups found. Ask: Were the properties correct?

Make a class list on the board of 3D shapes and their properties. Ensure the list includes cones, pyramids, spheres, cylinders and a range of pyramids

(including hexagonal prism, rectangular prism, cube and triangular prism)

E Worksheet: p10 Primary Mathematics Book D

R Blindfold a student and place a 3Dshape in their hands. The student tries to identify and name the shape by touch alone.

3D shapes

Worksheet

: p10 Primary

Mathematics

Book D

Lesson 2

Date

Focus: Name, sort and describe 3D shapes. Language Focus: cones, cylinders, prisms, spheres, properties, faces, edges and corners

O Play Celebrate Heads with three and four digit numbers. Revise yesterday’s lesson on 3D shapes: Discuss

edges, faces and corners

properties of prisms

properties of cylinders

G Students collect boxes, then cut and fold them to form nets. The nets of various prisms may be compared and discussed. The nets can be refolded

and the shape made inside out. Students could consider whether the same figure can have more than one net, eg consider which hexominoes can be

-celebrate

head bands

-variety of

boxes

-various nets

-worksheet

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm


folded to form a cube.

Students are given cut-out nets and asked to fold and glue to form the three dimensional shape.


R Show students pictures of nets and have them suggest the 3D shape.

p19 Primary

Mathematics

Book D

Lesson 3

Date

Focus: Draw and describe objects from various viewpoints Language Focus: three dimensional

O Have students counting forwards and backwards by tens or hundreds on and off the decade.

Ask: What does three dimensional mean? What are three dimensional objects? Discuss as a class.

G Hold up a cylinder so students cannot see the top of it. Ask students to pretend they are a bird flying above the cylinder and to draw what the bird

would see of the cylinder. When students have completed their drawings show them the top of the cylinder and check that they have drawn a circle.

E Students sit in a group close together, so they all have a similar view. Each student divides their whiteboard into four. Place an object in the front of

the class and ask them to draw, in the first box, what they can see of the object from where they are. Turn the object around so they can see and draw

the back of it, and then do the same for each side view. Discuss the drawings. Ask : What differences are there between the front view, back view and

each side view?

Have students play and experiment with a range of 3D objects. Ask them to show the tops, front and side views of the objects.

R Revise the names and properties of 3D shapes.

- 3D shapes

- whiteboards

& markers

Lesson 4

Date

Focus: Describe and make pyramids. Language Focus: faces, edges, corners/vertices and pyramid

O Have students counting forwards and backwards by tens or hundreds on and off the decade.

Give each group of four students some Polydrons. Ask them to use the four triangles to build a 3D shape. Ask: What is the shape called? (pyramids). Ask

students to describe some of the properties they can see: the number of faces, the number of edges and the number of corners (vertices). Ask: What

shape are the faces?

G Ask groups of students to use Polydrons to build another pyramid using a square and four triangles. Ask: How is it similar to the first pyramid? How is

it different? How many faces does the pyramid have? What shape is its base? Tell the students that pyramids are often named according to the shape

of the base, so this pyramid is a square pyramid. Ask: what is the name of the first pyramid that you made? (triangular pyramid). Ask groups to use a

hexagon from the Polydrons as the base for another pyramid and to build the pyramid and discuss the properties.

Compare triangular prisms and pyramids. Discuss how they are different (the prism has two opposite ends that are the same size and shape, the pyramid

- polydrons

-3D shapes

PowerPoint

- worksheet

p12 Primary

Mathematics

Book D


has one end and opposite that end is the apex where all the triangular sides meet at a point).

E Discuss the number of faces on a pyramid (the base and triangular faces). Discuss how the number of triangular faces relates to the shape of the

base (for example four sides in the base means that there are four triangular faces), Count and record the number of edges and corners.

Worksheet: p12 Primary Mathematics Book D

R Name the 3D shapes PowerPoint.

Lesson 5

Date

Focus: Investigate cross sections of 3D shapes Language Focus: three dimensional

O Play “what am I”? Say: I have 5 faces, 9 edges and 6 corners. My ends are triangular. What am I? (triangular prism). This helps to improve students’

visualisation skills. When a shape is identified, show students a model, so they can check its features.

G Students make prisms from clay, plasticine or playdough. By carefully cutting the models with a piece of wire or a knife, the cross-sections may be

studied. Students make various sections at right angles to the axis and note the results. They then predict the shapes resulting from cutting at an

oblique angle or cutting with a curved blade and perform the section to check their predictions.


R Revise the names and properties of 3D shapes.

-3D shapes

- Play dough &

wire or plastic

knives

-worksheet

: p13 Primary

Mathematics

Book D

Useful Websites:

Evaluation

&

Assessment





Can the students use accurate language to describe the features of a cylinder and a prism? Yes/ No


Can students match prisms and cylinders with their nets? Yes/No


Can students name the properties of 3D shapes? Yes/NO


Which students require remediation?

Which students require extension work?



7


40

Example:

45 - 8 =

9 + 28 =

+ 13= 40

52 - = 40



1. Cade had 11 marbles. He gave 3

to Dylan. How many does he have

left?

2. Michael has some fish in his fish

tank. Ben gave him 4 more fish. Now

he has 12. How many fish did he

have to begin with?

3. Alyssa had 5 cookies. Aiyanna

has 12. How many more cookies does

Aiyanna have than Alyssa?




Example: 10

2 x5 = 10 20 - 10=10

1 + 9 =10 40 ÷ 4 = 10






8




Example: 10

2 x5 = 10 20 - 10=10

1. Daniel had some noodles. He gave

12 noodles to William. Now Daniel

only has 4 noodles. How many

noodles did Daniel have to begin

with?

2. Hayley had 6 meatballs on her



e.g. 5429 = 5000 + 400 + 20 + 9




1 + 9 =10 40 ÷ 4 = 10






plate. Kirsten stole some of her

meatballs. Now she has 2 meatballs

on her plate. How many meatballs

did Kirsten steal?

3. Isabella’s hair is 18 cubes long.

If she gets a haircut and now her

hair is 9 cubes long. How much of

Isabella’s hair got cut off?



Term 1

Weeks 6 / 7

Statistics & Probability

Data


A student:

MA2-1WM : uses appropriate terminology to describe, and symbols to represent,

mathematical ideas

MA2-2WM : selects and uses appropriate mental or written strategies, or

technology, to solve problems

MA2-3WM : checks the accuracy of a statement and explains the reasoning used

MA2-18SP: selects appropriate methods to collect data, and constructs,

compares, interprets and evaluates data displays, including tables, picture graphs

and column graphs


ACMSP068 & ACMSP069

Conducts surveys to collect data and interprets the data gathered

Creates a simple table to organise data


Language: Students should be able to communicate using the following language: information, data, collect, category, display, symbol, list, table, column graph, picture graph,

vertical columns, horizontal bars, equal spacing, title, key, vertical axis, horizontal axis, axes, spreadsheet. Column graphs consist of vertical columns or horizontal

bars. However, the term 'bar graph' is reserved for divided bar graphs and should not be used for a column graph with horizontal bars.

Background Information Data could be collected from the internet, newspapers or magazines, as well as through students' surveys, votes and questionnaires. In Stage 2, students should

consider the use of graphs in real-world contexts. Graphs are frequently used to persuade and/or influence the reader, and are often biased. One-to-one

correspondence in a column graph means that one unit (eg 1 cm) on the vertical axis is used to represent one response/item. Categorical data can be separated into

distinct groups, eg colour, gender, blood type. Numerical data has variations that are expressed as numbers, eg the heights of students in a class, the number of

children in families


Revise 3, 4 & 6 times tables

Resources

Lesson 1

Date

Focus: Interpreting information presented in a table Language Focus: interpret, table

O Look at this table.

Discuss the table. What is it about? Consider students' ideas and see how they differ, e.g. students might:

suggest it is about how many girls and boys own a football or netball

tell you that the table does not have a heading

be able to suggest an appropriate heading, e.g. Choice of Sport.

G Ask: Are these the type of numbers you would expect to see in this table? e.g. Would you expect boys to have 10 footballs and 5 netballs? Ask

students to tell a story about the boys and girls in the table. Use these as examples:

... more girls play netball than football ...

... more boys play netball than football ...

... more girls than boys play football ...

... more boys play netball ...

... there are 13 girls and 15 boys ...

... there are 28 students altogether ...

- Note book

file with a copy

of the table


... there are 11 football players ...

... altogether 17 boys and girls play netball ...

... there are twice as many boys playing netball than football ...

Encourage students to ask questions about the given information, e.g. Why are there more boys than girls playing netball?

After this conversation, ask students questions which require them to make calculations using the information in the table. Support them to locate the

right information to answer correctly the question being asked.

E Students are asked to record the information from the table in a graph. Discuss with a partner the type of graph they would like to draw. Explain why

this is the best visual representation for them. Answers you might hear:

... because it is the easiest to draw ...

... because the columns are drawn next to each other and in different colours so they show all the information clearly

R Visit website below to create or read tables

http://www.ixl.com/math/practice/grade-4-read-a-table

Adjustment: questioning techniques

Lesson 2

Date

Focus: Use and interpret tally marks and read information from column graphs Language Focus: interpret, tally

O Revise yesterday’s lesson and brainstorm definitions for words related to data to display in the classroom.

G & E Display the column graph Chris's Bank Account from Supporting themes with mathematics. Give the students this information: Chris receives $5 in pocket money each week. This graph shows the amount of money in his bank account over 5 weeks.

- Note book

file with a copy

of the column

graph

http://www.ixl.com/math/practice/grade-4-read-a-table


In small groups students discuss the information in the table, then what each column shows. Discuss:

o What does the information along the vertical axis tell us? [the amount of money in his account]

o What does each marker represent? [50c] o Would the graph look different if each marker along this axis represented $1? How? o What does the information along the horizontal axis tell us? [the number of weeks he saved for] o How do the horizontal lines on the graph help us?

Write number sentences about each column, e.g.

o In week 1, Chris spent $3 and banked $2. [$5 - $3 = $2]

o In week 2, Chris had $2 and got $5 pocket money. [$2 + $5 = $7]

o However, he has only $1 in the bank, so he must have spent $6.

[$7 - $6 = $1]

Ask students to write a story about the information shown in the graph, and then share their stories with the class.

Students prepare questions based on the graph and place in a question box for the class to answer.

R Visit website below to create or interpret graphs

http://classroom.jc-schools.net/basic/math-graph.html

Adjustment: One on one support as needed

http://classroom.jc-schools.net/basic/math-graph.html


Lesson 3

Date

Focus: Constructing and interpreting a column graphs Language Focus: column

Revise language associated with graphing.

G & E Work with students to jointly construct a column graph to represent the class birthday months by following these steps.

Explain to students that the axes on a graph require a consistent scale and must be given appropriate labels.

Have students identify the scales (both vertical and horizontal) on a variety of graphs and determine what the axes represent. For example, are

they whole numbers, percentages, dates, ages, currency?

Demonstrate how to construct a column graph using the students' birth months.

a. On an IWB or normal whiteboard, write or type the title of the graph (e.g. Birthday distribution by month) and draw the axes

b. Label the vertical axis Number of students and the horizontal axis Month.

c. Place 12 markers equidistant along the horizontal axis. Write the months of the year between each of the markers.

d. Ask the students to write their name on a sticky note (or type it on IWB) and put it in the appropriate column on the whiteboard.

e. Consider the maximum number of birthdays in each month, then ask students to suggest a scale for the vertical axis.

f. Students use the information gathered to draw a column graph. Discuss and compare results.

Assist students in drawing meaning from graphs by demonstrating how to turn the information represented in the graph into sentences and

paragraphs.

R Students make statements based on information contained in the column graph, e.g. Most of our sample of birthdays occurred in May. In our sample, three months had exactly four birthdays occurring. In our sample, more birthdays occurred in July than in December.



Lesson 4

Date

Focus: Interpret and make tables Language Focus: table, most, least

O Make and model a class table on the board about the students favourite school subject. Write the categorises across the board and collect the data

either by tallying marks or by counting a show of hands. Discuss the results. Ask: Which subject is most popular? Which is least popular? How many more

students preferred maths to spelling?, etc

G As a class look at the features of the table at the top of the worksheet (page 59 Maths Plus 3). Choose different students to describe what the table

shows, then ask students to complete activity 10(a-d), Check as a class.

E Collect information regarding hair colour for your class. Discuss the tally scores and ask students to create a column graph of the results. Discuss

whether the graph shows the hair colour information more clearly than the table.

R After students have completed activities 11 and 12 on the worksheet; ask them to work in small groups to collect information about the favourite

winter sports of students in the class. Compare their results with those in the table on the worksheet.


- worksheet

Lesson 5

Date

Focus: Constructing and interpreting a column graphs Language Focus: column

O Play Count and Catch Fives – In pairs, students sit or stand about one metre away from each other, one with a ball or beanbag in their hand. The

student with the ball calla out the number five, as they toss the ball. The other student throws the ball back saying the number 10, and so on. How far

can they count in one minute?

G llllllllllll Draw a set of strokes on the board. Discuss the difficulty of counting many strokes and ask students

to suggest ways of making their counting easier. As a class, discuss the ways students travel to and from school and the safety

aspects of each method of travel.

E Ask students to conduct a survey to collect data on the different ways of travelling to and from school. Discuss the best way of recording the data

(e.g. as a tally). Discuss:

How are tally marks recorded? Why do you think tally marks are in groups of five?

Students collect and record their data in a table using tally marks.


Ask students to use this data to construct a column graph on graph paper. In small groups, students interpret the information in the graph. Ask questions

such as:

What is the most popular way of travelling to and from school? What is the least popular way of travelling to and from school? What is the safest method of travel? Why?

What safety considerations would you need to be aware of if catching the train; riding a bike; walking to school?

R Students compare results and make some general statements about their graphs.


Optional /

Additional

learning

experiences

1.Using Data

Use the data in a frequency table linked to a problem the class is trying to solve. Make – or use a computer to make – a simple bar chart, with the

vertical axis labelled in ones, then twos. For example:

Discuss questions such as:

- Which day had most/least packed lunches?

- How many packed lunches in the whole week?

- Why do you think there are different numbers of packed lunches brought on different days?

- Would next week’s graph of packed lunches be the same or different? Why?


computers


2. Test a Hypothesis

Test a hypothesis such as: We think that most children in our class walk to school. Decide what data is needed, collect it quickly then make – or use a

computer to make – a simple pictogram, where the symbol represents 2 units. Discuss questions such as:

- Do most children walk to school?

- More children walk than come by bike. How many more?

- How many children altogether in the class?

- How would the graph be different:

* if it were a wet day…? or December…?

* if there were no buses…?

* if we asked Year 6…?

Adjustment: One on one support as needed, questioning techniques

white board

and markers

Lesson 6

Date

Assessment task: Data

Useful Websites:


http://nces.ed.gov/nceskids/createagraph/default.aspx

http://www.primaryresources.co.uk/maths/mathsF1c.htm#bar

http://www.shodor.org/interactivate/activites/BarGraph/

Evaluation

&

Assessment

Have students had sufficient background experiences and discussion to be

able to carry out the planned activities successfully? Yes/No





Has the program been changed or modified in any way? Yes/No

If yes, how?

Can students use and interpret tally marks within data collections? Yes/ No


Can students read information from column graphs? Yes/No

Are students able to use the language associated with graphing? Yes/No

Can students interpret a variety of tables? Yes/ No


Can students create a table to display information they have collected? Yes/No

http://nces.ed.gov/nceskids/createagraph/default.aspx

http://www.primaryresources.co.uk/maths/mathsF1c.htm#bar

http://www.shodor.org/interactivate/activites/BarGraph/


Are students able to use the language associated with graphing? Yes/No

Other comments:



9


multiplication fact

Example:

2 + 2 + 2 + 2 =

4 lots of 2 +

4 x 2 =




1. Isabella’s hair is 18 cubes long.

By the end of the year her hair is

24 cubes long. How much hair did

she grow?

2. Jovana filled her bucket with 5

grams of shells. If she now has 28

grams of shells, how many grams did

she add?

3. Isha’s pencil is 12 cubes long. If

she sharpens it, now her pencil is 4

cubes long. How much did she

sharpen off of her pencil?




Example: 10

2 x5 = 10 20 - 10=10

1 + 9 =10 40 ÷ 4 = 10






10




Example: 10

2 x5 = 10 20 - 10=10

1. Mrs. Sheridan has 2 cats. How

many more cats does Mrs. Sheridan

need to have 20 cats?

2. Mrs. Sheridan has 2 cats. Mrs.

Garrett has 24 cats. How many

more cats does Mrs. Garrett have


50

Example:

55 - 8 =

19 + 22 =


1 + 9 =10 40 ÷ 4 = 10






than Mrs. Sheridan?

3. Mrs. Wong had 16 Valentines.

She gave 3 Valentines to her

children. How many does she have

left?

+ 13= 50

74 - = 50





Term 1

Weeks 8 /9

Fractions and Decimals


A student:

MA2-1WM: uses appropriate terminology to describe, and symbols to

represent, mathematical ideas


MA2-7NA: represents, models and compares commonly used fractions and

decimals


ACMNA058

Models and represents unit fractions including ½, ¼, a third and an eighth and their

multiplies to complete a whole.


Language Students should be able to communicate using the following language: whole, part, equal parts, half, quarter, eighth, third, fifth, one-third, one-fifth, fraction,

denominator, numerator, mixed numeral, whole number, fractional part, number line. When expressing fractions in English, the numerator is said first, followed

by the denominator. However, in many Asian languages (eg Chinese, Japanese), the opposite is the case: the denominator is said before the numerator.


In Stage 2 Fractions and Decimals 1, fractions with denominators of 2, 3, 4, 5 and 8 are studied. Denominators of 6, 10 and 100 are introduced in Stage 2 Fractions

and Decimals 2. Fractions are used in different ways: to describe equal parts of a whole; to describe equal parts of a collection of objects; to denote numbers (eg

is midway between 0 and 1 on the number line); and as operators related to division (eg dividing a number in half). A unit fraction is any proper fraction in which the

numerator is 1, eg

Three Models of Fractions Continuous model, linear – uses one-directional cuts or folds that compare fractional parts based on length. Cuts or folds may be either vertical or horizontal. This

model was introduced in Stage 1.

Continuous model, area – uses multi-directional cuts or folds to compare fractional parts to the whole. This model should be introduced once students have an

understanding of the concept of area in Stage 2.

Discrete model – uses separate items in collections to represent parts of the whole group. This model was introduced in Stage 1.



Revise 3,4 & 6 times tables.

Resources

Lesson 1

Date

Focus: Identify, represent and name fractions Language Focus: half, quarter, fraction

O Ask students what they know about fractions. Record responses on the board. Write a class definition of a fraction (for example: Fraction means part

of the whole number. A half is 1 out of 2 parts. Three-eighths equals 3 out of 8 parts). Look in Maths dictionaries to see how ‘fraction’ is defined there.


G Ask students to draw a square and shade half. Ask the students to draw a circle and colour half. Ask students to draw other shapes they know and

colour half each time. Display the shapes and check that the two parts shown in each shape are equal.

Model several fractions on the board. Ask students to write their own fraction and explain in writing (for example 4/8 means

____ parts out of _____). Students can draw an example of their fraction using shapes and shading.

Draw a shape on the board. Select one student to divide the shape into various parts (for example halves, quarter,etc). Select another student to colour

a certain section of the shape and then ask another to guess what fraction of the shape has been shaded.

E Worksheet: p 51 & 52 Primary Mathematics Book D

R Write 5/8 (or another fraction) on the board and give students two minutes to draw or make a representation of it. Look at each student’s

representation and check that the parts are equal. Allow students to comment on any that that they do not think are good representations.

- work sheet

- maths

dictionary

p 51 & 52

Primary

Mathematics

Book D

Lesson 2

Date

Focus: Find and represent fractional parts of a collection Language Focus: half, quarter, fraction

O Stand eight students in a row at the front of the room. Say: Half of the group kneel down. Ask other students how to say this mathematically ( ½ of 8

= 4)repeat for ¼ of 8, ½ of 10, ¼ of 12 and 1/5 of 10

G Give pairs of students counters or cubes. One student counts out 8 cubes. Say: Give half of the counters to your partner. How many counters did you

give your partner? (4) So, half of 8 is 4. Write this on the board ½ of 8 = 4.

Ask students to count out 5 cubes. Say: give one fifth of the cubes to your partner. How many did you give your partner? (1) So one fifth of 5 is 1.

Write on the board 1/5 of 5 = 1. Repeat this procedure for other numbers of cubes, asking students to find ½, ¼, and 1/5 of groups.

Demonstrate the strategy of using division to find a fraction of a number (for example 1/5 of 25 = 25 ÷ 5, which is 5)

E Worksheet: p 53 Primary Mathematics Book D

R Ask students if the strategy of using division to find a fraction of a number is effective. discuss as a class. Choose students to demonstrate the

strategy.

- cubes

- worksheet

: p 53 Primary

Mathematics

Book D



Lesson 3

Date

Focus: Find and represent fractional parts of a collection Language Focus: half, quarter, fraction

O Revise yesterday’s lesson of finding a fractional part of a collection

G Give pairs of student’s pop sticks or pencils and repeat yesterday’s lesson. Revise the strategy of using division to find a fraction of a number (for

example 1/5 of 25 = 25 ÷ 5, which is 5)

E Worksheet: p 91 Maths Plus 3 Student Workbook

R Play some of the games from the following website to consolidate students understanding.

http://www.bbc.co.uk/schools/ks2bitesize/maths/number

pop sticks and

pencils

Worksheet: p

91 Maths Plus

3 Student

Workbook

Lesson 4

Date

Focus: Dividing one whole into fractions Language Focus: half, quarter, fraction

O Students are given a worksheet with a large circle drawn on it. They imagine that the circle is the top view of a round chocolate cake (or pizza base)

which they have to share between five people. Ask: How would you cut the cake so you have five equal pieces and none left over?

Students draw lines on the 'cake' to show where the cuts would be. They could use pencils to work out where the cuts would be, before they

draw the cuts on the large circle.

Students discuss the strategy they used to cut the cake into five equal pieces. Discuss:

o If you have five equal pieces cut from one whole cake, what would each piece be called?

o What if the same cake was divided into ten equal pieces, so that each person could eat one piece and take one piece home. How would you change the five equal pieces into ten equal pieces?

worksheet

http://www.bbc.co.uk/schools/ks2bitesize/maths/number


o If you have ten equal pieces, what would each piece be called?

G & E Students are given three strips of paper of equal length.

Strip A represents one whole. Students write 'one whole' on the paper.

They fold strip B into fifths and label the strip 'fifths'.

They fold strip C into tenths and label the strip 'tenths'.

Students place the three strips of paper one under the other and discuss these questions

What can you tell about the size of each fraction?

What strategies did you use to create your fractions?

What strategies did you use to obtain equal parts?

Students use their folded strips of paper to count by fifths and tenths. They can complete the missing labels on worksheets showing fifths and tenths.

Write the missing fraction labels on these fraction strips.

R Revise language associated with fractions.


Evaluation

&

Assessment








If yes, how?

Can students identify and name halves, quarters and eighths? Yes/ No


Can students draw or model halves, quarters and eighths? Yes/No

Are students able to use the language associated with fractions? Yes/No

Can students use materials to compare fractions? Yes/ No


Can students find fractional parts of a collection? Yes/No

Are students able to use the language associated with fractions? Yes/No

Other comments:



9


multiplication fact

Example:

3 + 3 +3 + 3 =

4 lots of 3 +

4 x 3 =


counting and counters to make groups of

may be required by some students.

1. 6 birds were sitting in a tree. 4

more birds flew up to the tree. How

many birds were there altogether in

the tree?

2. Cindy’s mum baked 15 cookies.

Paul’s dad baked 12 cookies. They

both brought them to school for a

party. How many cookies did they

have altogether?

3. 18 children were riding on the

bus. At the bus stop, some more

children got on the bus. Then there

were 25 children altogether on the

bus. How many children got on the

bus at the bus stop?




Example: 10

2 x5 = 10 20 - 10=10

1 + 9 =10 40 ÷ 4 = 10








Term 1

Weeks 10 / 11


Volume and Capacity NSW Curriculum

Outcomes & Indicators A student:


mathematical ideas


MA2-11MG: measures, records, compares and estimates volumes and capacities

using litres, millilitres and cubic centimetres


ACMMG061

Recognises the need for a formal unit to measure volume and capacity

Estimates, measures and compares volumes and capacities (to the nearest litre)

Uses the abbreviation for litre(L)

Language:

Students should be able to communicate using the following language: capacity, container, litre, volume, layers, cubic centimetre, measure, estimate. The abbreviation

cm3 is read as 'cubic centimetre(s)' and not 'centimetres cubed'.

Background Information Volume and capacity relate to the measurement of three-dimensional space, in the same way that area relates to the measurement of two-dimensional space and length

relates to the measurement of one dimension. The attribute of volume is the amount of space occupied by an object or substance and is usually measured in cubic units,


eg cubic centimetres (cm3) and cubic metres (m3). Capacity refers to the amount a container can hold and is measured in units such as millilitres (mL), litres (L) and

kilolitres (kL). Capacity is only used in relation to containers and generally refers to liquid measurement. The capacity of a closed container will be slightly less than its

volume – capacity is based on the inside dimensions, while volume is determined by the outside dimensions of the container. It is not necessary to refer to these

definitions with students (capacity is not taught as a concept separate from volume until Stage 4). In Stage 2, students should appreciate that formal units allow for

easier and more accurate communication of measures. Students should be introduced to the litre, millilitre and cubic centimetre. Measurement experiences should enable

students to develop an understanding of the size of a unit, to estimate and measure using the unit, and to select the appropriate unit and measuring device. Liquids are

commonly measured in litres and millilitres. The capacities of containers used to hold liquids are therefore usually measured in litres and millilitres, eg a litre of milk will

fill a container that has a capacity of one litre. The cubic centimetre can be related to the centimetre as a unit to measure length and the square centimetre as a unit to

measure area.


Recite 3, 4 & 6 times tables

Resources

Lesson 1

Date:

Focus: Use informal units to estimate, measure and compare capacity Language Focus: capacity, volume, most and least

Capacity means: How much will an object hold? Volume means: The amount of space something takes up.

O Show students three different sized containers to the class. Ask: Which container would hold the most? Which container would hold the least?

Discuss the strategies for working out these answers. Students might estimate the largest container first. They could fill it with water and then pour

the water into the other containers. If the other containers are filled and some water is left, then the first container is the largest. Use a similar

procedure for working out the smallest container.

G Collect sufficient cups of different shape, size and capacity for each student to have one. Ask students to fill a bucket, large ice cream container or

bowl, using their cup. Count the number of cups used to fill the container. Students work in groups to construct graphs showing results for each person.

Discuss results with the group and the whole class. Repeat the activity using other informal units. For example, use teaspoons to fill cups.

Collect sufficient cups of the same shape, size and capacity for each pupil in a group to have one. Repeat the “Different Cups” activity. Discuss the

results obtained in the two activities. Graduate a larger container using the cups collected. Use this container to find the capacity of other containers.


R Revise the language associated with volume and capacity.

-various sized

containers,

cups, bucket,

ice cream

container &

teaspoons

-worksheet

Lesson 2

Focus: Understanding that capacity is measured in litres and millilitres Language Focus: capacity, volume, litres and millilitres


-various

containers

with labels

and


Date:

O Show students a range of containers with labels that hold different amounts of liquid. Say:

* I have a container and I want to know what its capacity is. Capacity means how much it will hold.

* Capacity is measured in litres or millilitres.

* Each container has a different capacity. Look at the labels to find out how much each container can hold.

* Students record list of containers and the capacity of each.

G Provide students with a list of cards with terms related to capacity.

In groups, students sort the terms into two columns.

E Show students a clearly labelled measuring jug and explains the measuring scales used to determine capacity (e.g. litre, 1 litre, 2 litres).The teacher

demonstrates how to measure capacity with the measuring jug by saying, If I pour liquid from this container into the measuring jug, I will know how much

it will hold – its capacity! I think (estimate) it holds about (approximately, nearly, almost) 2 litres.

R Visit website to consolidate students understanding of how to read measurements.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/measures/index.htm

measurements

-worksheets

-labelled

measuring

jugs

Lesson 3

Date:

Focus: Estimates and measures capacity in litres Language Focus: litre, millilitres


O Show students a variety of containers that hold one litre. Discuss other products they know of or they have at home that are available in lire

containers (milk, juice, detergent, etc)

G The teacher gives students a set of containers. Students estimate the capacity of each container and record their estimates in a table. After

estimating the capacity of each container, students use the measuring jug to find the actual capacity of each container and record it.

-various

containers

that hold 1

litre

( milk, juice,

detergent,

etc)

-worksheet



Students are given a variety of unmarked containers of various shapes and sizes. Students then select the container which they think will have a capacity

of 1 litre. Students test their prediction by pouring 1 litre of water into the container and record the capacity as being more than, equal to or less than 1

litre. Students collect a variety of containers with a capacity which is marked and less than 1 litre. Students then estimate the number of times this

container will have to be filled to equal 1 litre. Students check their estimate by filling and pouring into a 1 litre measuring container.


R Discuss the use of litres when measuring how much a container holds. Discuss when litres would not be a useful for measuring (doses of medicine, for

example). Discuss and compare different shaped containers that hold the same amount of liquid

- a variety of

unmarked

containers of

various shapes

and sizes

Lesson 4

Date:

Focus: Use cubic centimetres to construct models and calculate volume Language Focus: cubic centimetres, volume


O Hold up either a shoebox or a chalk box. Ask students to estimate how many of the blocks will fit into the box and record their estimate. Choose a

student to pack the box with blocks and count as they pack. Ask: Whose estimate was closest? Hold up the other box and ask: Will it hold more or less

than the first box? Students estimate and check, as for the first box.

G Give each student 12 cubes and ask them to model with the cubes touching each other fully along one side. Look at the different models that are the

same shape together. Ask: How many different shapes have we made from 12 cubes?

Ask the students to construct a variety of different shapes from centicubes or Base 10 ones. Ask: How many centicubes are needed to build each shape?

Discuss how each centicube has sides that measure 1cm. Each centicube is therefore, a cubic centimeter. Hold up one of the models, count the number of

centicubes used to build it and say, for example: This shape was made up with 9 centicubes; therefore its volume is 9 cubic centimetres. Write it on the

board so that students can see how it is recorded (9cm3). Have students say the volume of their own shape.

Focus students’ attention on any rectangular prisms that were constructed. Select a shape that has several layers. Carefully disassemble the shape,

taking off one layer at a time. Ask students to determine how many blocks are in the first layer. Then replace the blocks one layer at a time and ask the

- shoe box or

calk box

- cubic

centicubes

-worksheet


students to skip count to keep track of how many blocks made up the whole shape.

Revise the idea of ‘how many in one layer’. Then students should consider the number of layers there are. They can use these two ideas to work out the

total number of blocks used to make each prism.

E Worksheet: p109 Maths Plus 3 student workbook

R Visit website to consolidate students understanding of how to read measurements.


Lesson 5

Date:

Focus: Measure and compare the volume of models made with cubic centimetres Language Focus: cubic centimetres, volume


O Discuss students understanding of the words volume, capacity and the measurements used for measuring (millilitres, litres and cubic centimetres)

G Ask students to make the models pictured in activity 10 on page 139 of the Maths Plus 3 student workbook, one at a time, and record the volume of

each. As the students are making the models, check they realize there are some cubes which cannot be seen in the drawings. Ask students to describe

how they counted the cubes, particularly for models that have several layers.

E Have students make shapes of specified volume. For example ask them to: Build a model that has a volume of 10cm3. Compare all the models and put

those that look the same together. Ask: How many different models have been made with a volume of 10cm3? Ask students to use 12 cubes to make a

model and then draw it. Share the drawings and discuss the techniques students used to draw models. Allow students to practice drawing other models

that have a volume of 12 cubic centimetres.

R Look at questions from previous Naplan papers relating to volume and capacity and discuss how students would go about answering the questions.

- cubic

centicubes

-worksheet

Lesson 6

Date:

Focus: Measure and compare the volume of models made with cubic centimetres Language Focus: cubic centimtres, volume


O Review ideas of capacity as the amount of liquid a container can hold and volume as the amount of 3D space inside an empty container or the amount of

solid matter that makes up a solid object.

• Show students a Base 10 one block and explain how this is a cubic centimetre, i.e. it is a cube that measures 1 cm in length, width and height.

• Show how a Base 10 ten block (or rod) has a volume of 10 cubic centimetres (cm3).

• Show how a Base 10 hundred block (or flat) has a volume of 100 cm3.

• Show how a Base 10 thousand block is like a big cube with a volume of 1000 cm3. Demonstrate that the hundreds block would cover the base of this and

that ten flats would stack up in height to make the big cube.

• Show that the thousand block measures 10 cm in length, width and height and that 10 x 10 x 10= 1000.

• Use the NTI ( Nelson Teaching Interactive Software 3)to illustrate stacking cubic centimetres to determine the volumes of various

- cubic

centicubes

Nelson

Teaching

Interactive

Software 3



rectangular prisms.

G Use Base 10 one blocks or connect cubes to build models of rectangular prisms as they are shown on the NTI. Count the number of blocks to determine

the volume of the prism. Play the game on the software

E Have students complete worksheet p71 Primary maths Student activity Book 3

R Have students solve the following questions:

A blue bucket holds 6 litres and a green bucket holds 7 litres.

1. How many litres do both buckets hold altogether?

2. How many litres would four green buckets hold together?

3. How many blue buckets are needed to fill a 60 lire container?

4. How many green buckets are needed to fill a 42litre container?

When a toilet is flushed, about 8 litres of water is used. Have students use mental strategies to calculate how much water is used in:

1. Three flushes

2. Five flushes

3. Seven flushes

4. Eight flushes, etc

Lesson 7

Date

Assessment task: Volume & Capacity

assessment

task

Useful Websites:

http://pbskids.org/cyberchase/games/liquidvolume/liquidvolume.html

http://www.bbc.co.uk/skillswise/numbers/measuring/volume/index.shtml

Evaluation



Can the students arrange a variety of containers from smallest to largest capacity? Yes/ No

http://pbskids.org/cyberchase/games/liquidvolume/liquidvolume.html

http://www.bbc.co.uk/skillswise/numbers/measuring/volume/index.shtml


&

Assessment

Did I organise sufficient equipment for all students to be actively involved in

group work? Yes/No

Did I encourage students to make use of the playground for these water

activities?


If yes, how?


Can students make reasonable estimates of capacity? Yes/No

Can the students construct models from centicubes and work out the volume in cubic centimetres? Yes/ No


Can students count cubes to calculate volume? Yes/No

Can students make models to specific volumes? Yes/No

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