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PIALBA STATE SCHOOL: MATHEMATICS YEAR 5 SEMESTER 1 UNIT 1 PLAN

Proficiency Strands

At this Year level:

• understanding includes making connections between representations of numbers, understanding includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry

• fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles

• problem-solving includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans

• reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets.

Pedagogical Practices Levering Digitally Learning Environments Learning PartnershipsPedagogical Practices are used to design, monitor and assess learning.

Leveraging digital accelerates access to knowledge beyond the classroom and cultivates student driven deep learning.

Learning Environments foster 24/7 interaction in trusting environments where students take responsibility for their learning.

Learning Partnerships are cultivated between and among students, teachers, families and the wider environment

Continual Feedback loop / monitoring

Deep Learning opportunities through open-ended questioning and tiered tasks using Collaboration: Elbow partners, small groups, whole class, Innovation Space, Computer lab.

Check in / Check out (thumbs up) strategies

Deep Learning Competency Focus: (Focus from 2019 beyond other than Year 4 NPDL Planning 2018)Collaboration Creativity Critical Thinking Citizenship Character Communication

1 of 57Mth_Y04_U1_AT_MathGuidedInquiries

Assessment (D – Diagnostic, M- Monitoring, S – Summative)Week D-F-S Assessment Title

1 D Show Me Term 1 Pre-Test

3 S Interpreting Data and Posing Questions to Collect Data

4 M/ S Guided Inquiry: Investigating Chance Experiments

6 S Solving Simple Multiplication, Division and Fraction Problems

8 M Converting Between 12- and 24-Hour Time

9 M Finding the Area of Rectangles

9 M Finding the Perimeter of Rectangles

10 D Show Me Term 1 Post-TestShow Me Term 2 Pre-Test

Planning is sequenced across the Term or Semester. Timings of units are based on data and school timetabled events.

Key Learning Area: Maths

Year Level Team: Year 4 Term: 1Show Me Pre-test is to be completed, entered into Spreadsheet and

unpacked with Year Level teachers prior to the commencement of the UnitWalt / Wilf / Tib(The What)

Active learning Engagement(The How)

Check for Understanding Differentiation ResourcesALL RESOURCES HAVE BEEN UPLOADED TO ONENOTE

NUMBER AND PLACE VALUERounding

#Warm Ups Rounding Rodeo Get Closer# Number TalksEstimate: 1 240 × 3 = 4 500 × 4 = 42 876 × 3 =

#ActivitiesRounding: Large number track drawn on the ground, identify

benchmark numbers 0 and 10 and the halfway mark of 5. Roll a 10 sided dice, stand on that number and decide if it is quicker to run home or run to the target

Apply rounding to nearest 10, 100 and 1000. (number tracks can be changed to represent tens, hundreds and thousands)

Apply rounding to nearest 10 using decimal numbers (32.45 rounded to the nearest 10)

Students will apply rounding and estimation in addition/subtraction and multiplication/division

throughout the unit. This will be important for working efficiently and checking reasonableness of answers

particularly in assessment

Do students consider the correct place value place

when rounding to 10s (ones), 100s (tens) and 1000s

(hundreds)

Students can have a misconception that they need

to look at the last number when rounding. Therefore

when rounding decimals, will not consider the ones place

L2B

Allow 'wait time' for the student to process information

Explicitly teach the vocabulary to ensure the students have the required prior knowledge.

Provide smaller number of vocabulary words and use picture clues with explanation.

Plan for visual supports to instruction.

Break tasks into smaller, achievable steps.

Use small group instruction and cooperative learning strategies

Use technology to record students work; e.g. digital photography, tape and video.

U2BReading calendars

Linking months of the year to seasons

Expose to more technical or specific Maths vocabulary.

Extend with students choice of extra study – ensure one-to-one conferences to allow student to share their work.

Use computers to reduce the additional practice of concepts and skills – Compact the curriculum where possible.

Independent Work

Peer Instruction

Tiered tasks

C2C Digital Maths Library:

https://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-5cb2-4db6-8fd2-43d3563ffe8a/1/Mathematics_Library/index.html

Dice Four Square Mats Number Expanders Place Value Mats MABs whiteboards and markers

Languageround, closest, nearest, place value, ones, tens, hundreds, thousands, efficient

Walt: Round numbers to the nearest

10, 100 and 1000

Wilf: using benchmark numbers using place value parts to

round correctly

Tib: Using rounding helps us to

estimate and check the reasonableness of our answers






Key Learning Area: Maths Year Level Team: Term: 1

Walt / Wilf / Tib(The What)

Active learning Engagement(The How) Check for Understanding Differentiation Resources

NUMBER AND PLACE VALUEAddition and Subtraction

#Warm ups Rounding Rodeo Get Closer

#Activities Explicit Lesson: Left to Right Method Addition

Model with regrouping also

Explicit Lesson: Left to Right Method Subtraction

Model with regrouping also

Students need a firm understanding of place value in order to add and subtract

using this method

L2B






Use small group instruction and cooperative learning strategiesUse technology to record students work; e.g. digital photography, tape and video.

U2BReading calendars

Linking months of the year to seasons




Independent Work

Peer Instruction

Tiered tasks



MABs Place Value Mats dice whiteboards

Languageaddition, subtraction, estimate, round, place value, regroup, strategy, reasonable

Walt: Add and subtract numbers using the ‘left to right written’ method

Wilf: Using place value parts correctly to add and subtract

Tib: This method is the beginning of the formal written method and represents place value parts





Solve a range of addition and subtraction number sentences and number stories. Estimate first, check for reasonableness

If required, provide students with MABs and place value mats to represent numbers concretely and with numbers

#Open Ended 2 □6 + □8 = □2□Work out all possible answers for this addition □□□□ + □□□□ 5 0 0 0

What might the missing numbers be?






Check for Understanding

Differentiation Resources

NUMBER AND PLACE VALUE

Multiplication and Division

#Warm ups Rounding Rodeo Get Closer#Number Talks 7 x 432 = 1321 x 4 = 3194 x 2 = #ActivitiesMultiples and Factors Explicit Lesson: Multiples and Factors – create a display poster (see Factors

and Multiples Display Poster) explore multiples of 2, 3, 5 & 10 in a variety of ways

o Skip count on a number lineo Around the World gameo Buzz gameo Highlight multiples on a hundred board (see Learning Object – Hundred

Board and Calculator Combo.) Find common multiples of numbers o Calculator – count in multiples

Practice Time Tables:o Sing Times Table Songso ROTE learningo concrete materials

Use Multiplication Grid (and Learning Object) to find factors

Find Factorso Use list of known multiplication facts to find missing factors (inverse

relationship)

o Use calculators to divide multiples and find factors Explicitly Teach how to find common factors Discover divisibility rules for numbers (use hundred grid) Make posters

showing the divisibility rules for each number (See Divisibility Rules Poster) PPT – Factors and Multiples Quiz Maths Mastery Challenge Cards Multiples and Factors

Check that students understand the

language of multiples and

factors

Can students describe the relationship

between pairs of numbers (i.e. 3 and

27)?

Can students identify factors

using known number facts?

L2B






Use small group instruction and cooperative learning strategiesUse technology to record students work; e.g. digital photography, tape and video.

U2B




Independent Work

Peer Instruction

Tiered tasks



Hundred boards Learning Object:

Hundred Board Factors and Multiples

Display Poster Time Table Songs Maths Sing It!:

Multiplication Songs Divisibility Rules Poster Sheet Multiplication

Grid Learning Object:

Multiplication Grid Calculator PPT – Factors and

Multiples Quiz Maths Mastery

Challenge Cards Multiples and Factors

Multiplication Flash Cards

Languagefactors, multiples, multiplication, division, divisible, common, relationship, efficient strategy, compensate strategy, split strategy, place value, partition, inverse relationship, reasonable, estimate, rounding, number sentence, number story, word problem

Walt:Understand the relationship between factors and multiples. We are also choosing an efficient way to multiply numbers

Wilf:Using a range of strategies to identify multiples and factors and choose an efficient and effective strategy for mulplication





Tib:We need to be able to multiply numbers and have an understanding of their relationships

Multiplication and Division Explicit Lesson: Split Strategy Multiplication and Division

o model how to round numbers to estimate a reasonable answero model think aloud to use split strategy

Explicit Lesson: Compensate Strategy Multiplication and Divisiono model how to round numbers to estimate a reasonable answero model think aloud to use compensate strategy

Provide multiple opportunities for students to practise split and compensate strategies (use Multiplication Flash Cards for stimulus or use as a basis for word problems). Model number sentences and number stories (word problems)

#Open EndedA school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus?

Ensure students are able to partition accurately into

place value parts

Do students check their answers for reasonableness?

Can students explain their choice of

strategy?








FRACTIONS AND DECIMALS

Comparing and Ordering Fractions

#Warm ups Fraction Strip Game#ActivitiesModel and compare unit fractions: Draw, compare and order the size of unit fractions

using shapes or grids Sheet: Unit Fraction Models Sheet: Fraction Match and Order Unit Fractions Compare Fractions with Dominoes

o draw random dominoes and order least to greatest

o Domino War – game for two (or more) draw random dominoes. The person with the largest fraction wins both dominoes. Most dominoes at the end wins

Fractions of Collections PPTs (encourage answers using unit fractions)

o Fractions in Dot Patternso Fraction in Tile Patterns

Use hands on materials to find unit fractions of collections (i.e. use 12 counters find ½, 1/3, ¼, 1/6, 1/12) – when unit fractions are found, students can find other fractional amounts (i.e. 2/3)

Worded Problems: Safari Park Fractions Differentiated

BUILDING FOR ASSESSMENT

Do students understand what a unit fraction is? An

explicit lesson may be required? (PPT Compare

and Order Fractions may be useful)

Students should have an understanding that the larger the denominator

in a unit fraction, the smaller the fraction

Collections: Infer that as the number of equal

parts increases, the size of each portion

decreases.

Develop Fluency by asking: What is the repeating

L2BAllow 'wait time' for the student to process informationExplicitly teach the vocabulary to ensure the students have the required prior knowledge.Provide smaller number of vocabulary words and use picture clues with explanation.Plan for visual supports to instruction.Break tasks into smaller, achievable steps.Use small group instruction and cooperative learning strategiesUse technology to record students work; e.g. digital photography, tape and video.

U2B




Independent Work

Peer Instruction

Tiered tasks



Fraction Strip Gameboard (place inside swipe and wipes for multiple use)

10 sided dice whiteboard markers PPT Compare and Order

Fractions whiteboards Sheet: Unit Fraction

Models Sheet: Fraction Match and

Order Unit Fractions Safari Park Fractions

Differentiated Sheet PPT Fractions in Dot

Patterns counters, buttons,

jellybeans, smarties, etc. Learning Object: Number

Line Blank 0-10 Number Lines Blank 0-20 Number Lines Sheet – Exploring Patterns

in Fractions Determinator Game sticky notes drinking straws or paddle

pop sticks

Languagefraction, unit fraction, model, represent, equal parts, whole, portion, denominator, numerator, quantity, compare, order,

Walt: Compare and order

unit fractions. Identify unit

fractions as greater than/less than 1

Wilf: Using equal parts to

partition fractions locating fractions on

a number line counting on and

back by unit fractions up to 2

Tib: Comparing fractions and locating them on a number line helps to build a visualisation of the size of fractions in





relation to each other. SheetFractions on Number Line Count by unit fractions on a number line over 1 (i.e.

start at 1 and count on in sixths – 1 and 1/6, 1 and 2/6 etc) – Blank 0-10 and 0-20 Number Lines have been provided in resources

Learning Object: Number Line – use to count in fractions. Identify fractions on the number line, identify one more, one less etc

Compare fractions Whole class – Fraction Benchmarks

o Large blank number line on board. Give students sticky notes with fractions written on. Place in correct positions on number line. JUSTIFY placement

Sheet – Exploring Patterns in Fractions Play “Determinator” Game – see resources for

instructions

Fractions Greater Than 1 Using a number line, count on in unit fractions over 1.

Discuss fractions that are more than 1, less than 2, how many thirds make 1 etc.

Use concrete materials (drinking straws or paddle pop sticks) to measure increments of 1 on a number line string. Count on and back in unit fractions using pegs and/or sticky notes to create marks as increments

#Open EndedHow many different ways can you show 2/3?

pattern? (It’s a cross made up of 1 blue tile and 4 red tiles)

How many tiles are in each repeating pattern? (5 tiles)

What fraction of the pattern is one tile? (1-fifth)

How many tiles in a pattern are blue? (One)

What fraction of the pattern is blue? (1-fifth)

What fraction of the pattern is red? (4-fifths)

Some students may realise the relationship between fractions and division/multiplication. If they don’t see that, allow them to work using models and concrete materials.

Can students recognise the distance between zero and one as a unit?

Can students identify that a unit can be subdivided into fractional parts?

Using 2 concrete items to from a line can be a less

abstract way of demonstrating fractions on a number line, greater than

1, to students.


Key Learning Area: Maths Year Level Team: Term: 18 of 57Mth_Y04_U1_AT_MathGuidedInquiries





FRACTIONS AND DECIMALSAdding and Subtracting

Fractions

#Warm ups Fraction Strip Game

#ActivitiesAdding Fractions Slideshows:

o Adding Fractions Using Circles (use accompanying sheet)

o Joining Fractions that Make 1 Wholeo Adding Fractions that Total a Number

Greater than 1o Adding Fractions

Subtracting Fractions Slideshows:

o Subtracting Fractions Using Number Line (Use accompanying sheet)

o Subtracting fractions and identifying a unit fraction

o Subtracting fractions Work in groups to solve Addition and

Subtraction Fraction Problems

#Open Ended

❑5

+❑5

=❑5

ASSESSMENT: Solving Simple Multiplication, Division and Fraction

Problems

Check that students make note of like-denominators

before attempting to add or subtract fractions.


U2B




Independent Work

Peer Instruction

Tiered tasks



SlideShows:o Adding Fractions Using

Circles (use accompanying sheet)

o Joining Fractions that Make 1 Whole

o Adding Fractions that Total a Number Greater than 1

o Adding Fractionso Subtracting Fractions

Using Number Line (Use accompanying sheet)

o Subtracting fractions and identifying a unit fraction

o Subtracting fractions Addition and Subtraction

Fraction Problems

Languagelike denominator, addition, subtraction, fraction, numerator, denominator, common fraction, count on/back, strategy, unit fraction Walt: Compare, count, order and add proper fractions, represent unit fractions using materials and diagrams and solve subtraction and addition fraction problems

Wilf:Modelling of fractions using diagrams and number lines and solving addition and subtraction problems with fractions

Tib: To have a deeper understanding of fractions and how they are represented.











DATA REPRESENTATION AND INTERPRETATIONRepresenting and Interpreting Data

#Warm ups#Activities Display a wide range of visual data examples.

Have student examine and discuss “What is data?” Create a class definition

Make explicit the purpose of data (e.g. who might use the data and why).

Investigate different types of data and the best ways to display this data

o numericalo categorical

Create anchor charts with suggested examples that fit as numerical data or categorical data

Data Display posters – discuss the different data displays and data they might represent. Be explicit about graphing conventions – in particular column graphs

Use sheet “class survey” to collect class datao discuss who might need this data and

whyo create frequency tableso create columns graphs – digital graphs

can be created using Learning Object “Graph Maker 2”

o write summary statements about the salient information in graph

Year 5 Data Interpretation Warm Up PPT

Interpreting Data Link to reading comprehension – literal,

inferential and critical. I Do, We Do, You Do – pose questions at the three levels based on given graphs (see resources ‘Column and Picture Graphs’ and ‘Take-away Food Data’). e.g.

ASSESSMENT:Interpreting Data and Posing Questions to

Collect Data

Check that students understand the different between categorical or numerical data

Are students able to interpret the data in graphs to draw conclusions?

Students should be able to identify the salient information in data and provide a statement to summarise. If this is not being achieved, and explicit lesson may be required.


U2B




Independent Work

Peer Instruction

Tiered tasks



Sheet – Assorted Data Images poster paper and markers Sheet – Class Survey Sheet – Column and Picture

Graphs and Sheet – Take-away Food Data Learning Object – Graph

Maker 2 Sheet - Dot Plot Data

Interpretation Differentiated Year 5 Data Interpretation

Warm Up PPT

Languagedata, display, table, graph, bar graph, column graph, dot plot , frequency table, tally marks, numerical data, categorical data, graphing conventions, title, x/y axis, horizontal/vertical axis, column, categories, summary statement, Walt: Gather and interpret data and pose questions to gather data.

Wilf: Formulate questions to relate to interpreted data

Tib: We gather data to inform decisions we make





Dot Plots Explicitly teach Dot Plots – used to display

numerical data Whole Class – Dot Plot Data Interpretation

Differentiated Sheet (choose appropriate level) Create Dot Plots from previously collected data

#Open Ended What might this graph represent? Complete the

labels on the graph.








CHANCE#ActivitiesIdentify Outcomes as Fractions

List the possible outcome of tossing a coin. (heads, tails) explain that to toss a tail is 1 outcome out of 2 possible outcomes and link directly to fractions

Game – Greedy Pig

Inquiry Question:‘Is the three-player version of rock paper scissors fair?’

Follow the Mathematical Inquiry Method outlined in the resource Investigating Chance Experiments

Establish learning context Consider the game (Discover) Review the Mathematical guided inquiry

process (Discover) Prepare to implement (Devise) Develop responses (Develop) Present inquiry responses (Defend) Explore further learning opportunities

(Diverge)

GUIDED INQUIRY: Investigating Chance

Experiments

Students will be required to apply their mathematical

understandings of probability and data collection to conduct

experiments. Students understanding should be

monitored throughout this process


U2B




Independent Work

Peer Instruction

Tiered tasks



coin dice Greedy Pig Game Play Greedy Pig Game Board Sheet: Investigating

Chance Experiments (GI)Thinking About 3-Player Rock Paper Scissors

Languagefraction, outcome, probability, ‘out of’, chance, favourable outcome, fair, dependent and independent events, experiment, Walt: Use Fractions to represent the likelihood of an event occurring

Wilf: Identify all possible outcomes in chance experiments, describe the probability of outcomes occurring using fractions and describe chance experiments using the language of chance

Tib: We need to understand that fractions express the chance of an event happening





MEASUREMENTTime

#Activities Clock Display: 12-24 Hour Flower

o display 24 hour times around standard classroom clock for easy reference

Explicit Lesson: Converting to 24 hour timeo add 12 hours from 1pm to 11 pmo how 24 hour time is displayed o how 24 hour time is read

Create an anchor chart – 12 and 24 hour reference

Display sheet ‘Airline Schedule’ – discuss and practise reading 24 hour time with minutes i.e. 18:40 = eighteen forty hours

Whole class: PPT – 12 and 24 Hour Clock Conversion

Complete Monitoring Task - Converting between 12- and 24-hour time.

#Open EndedThe time is now 20 minutes after 3 o’clock. Show this time in as many ways as you can.

Monitoring Task:Converting between 12-

and 24-hour time

Can the student: Read and represent

24-hour times? Convert am and pm

times to 24-hour time?


U2B




Independent Work

Peer Instruction

Tiered tasks



12-24 Hour Flower Clock Display (NB a 00 instead of 24 can be found at the end of the resource)

PPT: 12 and 24 Hour Clock Conversion

12 and 24 hour reference Chart

Languagetime, 24 hour, 12 hour, ‘hundred hours’,

Walt: Convert between 12 and 24 hour time

Wilf: 24 hour time for after

midday using correct language to

read 24 hour time ‘add 12 hours’ to pm time

Tib: 24 hour time is used in a variety of contexts in our everyday lives











MEASUREMENTArea and Perimeter

#Warm ups Area/Perimeter Dice Game2-player game. Roll dice to determine length of sides. Draw the rectangle on square cm paper and colour in the area made. Play continues until there is no room left.

#ActivitiesPerimeter:

This is students’ first introduction to perimeter. Work with just rectangles and squares

to build understanding initially Identify the term ‘perimeter’ and its meaning

‘peri’ meaning around and ‘meter’ meaning to measure. Discuss “What is a boundary?” Co-construct a joint understanding (definition) and anchor chart to display in the classroom.

Identify square and rectangular shaped objects within the classroom (desk, classroom, whiteboard, pencil case, book etc). Have students run their fingers around it to become familiar with the idea of perimeter.

Find a large area outside (e.g. basketball court). Estimate the length of the sides. Step it out with strides, adjust estimates and calculate the perimeter around. Repeat with another large area. Repeat using smaller objects in the classroom (estimate first) and calculate.

Geoboards:o Make squares and rectangles and

count the number of spaces around to calculate perimeter

Measure lengths of the sides of rectangles in the classroom. Calculate the perimeter using formal measurements. Students should explain their processes.

Area:

Monitoring Task:Finding the Perimeter

of Rectangles

Do students understand the real world purpose of measuring perimeter (fences, picture frames, racetrack etc.)?

Be specific about the terms: closed shape, parallel, opposite sides. Check that students have the prior knowledge that rectangles and squares have parallel sides with the same length.

Students should be able to make reasonable estimations using familiar referents (strides, finger lengths, height etc). This is a skill that is needed in our daily lives and should be encouraged prior to measuring.

Students are not expected to use formulas to calculate perimeters at this stage

Monitoring Task:Finding the Area of

Rectangles


U2B




Independent Work

Peer Instruction

Tiered tasks



tools for measuring length: rulers (30cm, 1m), trundles, measuring tapes

variety of square and rectangular shaped objects from the classroom

geoboards and rubber bands

Learning Object: Geoboard 1cm dot paper dice

Languagelength, width, boundary, closed shape, sides, opposite sides, parallel, 2 dimensional (2D), square, angles, metre, centimetre, square metre/centimetre Walt: Understand the term

perimeter and measure perimeter using estimation and formal measurements

Understand the term area and measure area using formal measurements

Wilf: Finding the perimeter of a

variety of different rectangles

Students using the language of closed shape, parallel, opposite sides.

Tib: Knowledge of perimeter and language used will help when students have to calculate perimeter.





Create an area anchor chart to display. Discuss measurements in square centimetres and metres.

Measure the area of surfaces in the classroom using informal unit (envelopes, tiles etc)

Use 1cm dot paper to create demonstrate a square centimetre. Use rulers and masking tape to demonstrate 1 square metre in the classroom.

Have students use rulers, newspapers and masking tape to create square metre templates

Use 1sq m templates to measure large carpet areas. How many squares for each length and width? Discuss how to use this information to calculate the total area.

Use 1cm Square Paper to draw rectangles and squares and calculate the area. (encourage students to label sides with cm measurements

Challenge students to draw a variety of shapes that have an area of 16sq cm (this does not have to be only squares and rectangles)

#Open Ended I am thinking of something in the classroom that

is larger than 1sq m. What might it be?I am thinking of something that is smaller than 1sq m. What might it be?

Demonstrate how to abbreviate one square

metre to 1 sq m. (Use of the superscript 1 m² is introduced later in the

year.)

Ensure students readily differentiate between perimeter and area.


ASSESSMENT

Modified 16.11.18 Year 5 Unit 1

Assessment task — Interpreting data and posing questions to collect data

Name Date

1. Below is data collected about temperatures in Calgary, Canada.HINT: A temperature with a negative symbol (-) beside it is below zero.

Use the table to answer the questions below.a) What are the maximum and minimum temperatures for the month of May?

_______ max _______ min

b) Which months had a maximum temperature of 20 degrees and above?

____________________________________________________________________

c) What is the difference between the minimum and maximum temperatures in August?

__________________________________________

2. Examine the table and answer T (TRUE) or F (FALSE) for each statement.

a) January and November had the same maximum temperature. _____b) August is the hottest month of the year. ____c) A family want to visit Calgary when it is warm. Which two months would be the best time for them to

travel to Calgary?

______________________________________________________________________________________

________________________________________________________

d) Explain your answer.________________________________________________________________________________________

________________________________________________________________________________________

________________________________________

3. Examine this data about homework habits of Year 5 students and answer the questions below:

a) How many children never do their homework?

____________________________________

Year 5 Homework Habits

Key: = boy = girl

N u


b) How many children are in the class?____________________________________

c) Write three statements that include a comparison.(i) _________________________________

__________________________________________________________________

(ii) _________________________________

__________________________________________________________________

(iii) _________________________________

mbe

r of s

tude

nts

Never do it

Usually do it

Always do it

4. Read the graph of Year 5 data collected.

a) What is an appropriate type of data display to represent the data in this table?_________________________________

b) Construct the graph.


c) Explain why this data display is an appropriate representation.

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________

Data is information. Our world is full of information. To deal with this information and understand things better, we ask questions, collect information and organise that information or data.

5. Our class is trying to win the attendance award. Pose a question that will collect information about your class attendance.

_________________________________________________________________________

_________________________________________________________________________


Question 5

We can collect numerical data (data that involves numbers or amounts) or we can collect categorical data (data that involves things such as objects or preferences).

a) What type of data do these questions collect?

If the question collects numerical data, write N in the box beside it.If the question collects categorical data, write C in the box beside it.

How many pets do you have at home? What is your last name?

Which is your favourite sport? How many tries did the Broncos score?

Data is often collected by surveying groups of people (e.g. a bakery might survey adults to find the type of bread they most regularly eat).

b) Complete the table below by writing different questions that could be used to collect categorical data and numerical data for the groups listed.

Groups Numerical data (numbers) Categorical data (things or preferences)

Year 5 Students

Tourists

Question 7

This graph shows the favourite takeaway foods of Year 5 students.


Question 6

Here is the same graph without a title, scale or labels.

a) What other set of data might this graph represent? _______________________________

b) Add an appropriate title, scale and column labels to the graph to reflect the new data set.

c) Write a summary statement that is supported by the data in the new graph.


Pies Burgers Fish and chips

Pizza Chinese Sushi Chicken0

5

10

15

20

25

30

Favourite takeaway food

Year 5 Mathematics: Unit 1 — Interpreting data and posing questions to collect data Name:

Purpose of assessment: To classify and interpret data, pose questions to gather data and construct data displays appropriate for the data.

Understanding and Fluency Problem solving and ReasoningClassify and interpret data.Construct appropriate data displays.

Pose questions about data in context.

Writes comparative statements using data from a dot plot. 3c

Poses questions to gather categorical data and numerical data for different groups of people. 6bCreates a new set of data to match a given column graph and writes a summary statement. 7a-c

A

Interprets complex data in a frequency table. 2bWrites a comparative statement using data from a dot plot. 3cConstructs an appropriate data display, accurately applying graphing conventions. 4b

Explains choice of data representation by referring to features of chosen graph. 4cPoses questions to gather numerical data and categorical data. 6b

B

Interprets data in a frequency table. 1a, b, c, 2a, cInterprets data and writes a statement using data from a dot plot. 3a, b, cConstructs an appropriate data display. 4a, bClassifies questions as collecting numerical or categorical data. 6a

Explains conclusions using data in a frequency table. 2dExplains choice of data representation 4cPoses questions to collect data about groups of people. 5, 6b

C

Interprets some data in a frequency table. 1a, b c, 2a, b, c Classifies some questions as collecting numerical or categorical data. 6a Poses a question about a group of people. 5, 6 D

Answers a question about data. Poses a question that asks for information. 5, 6 E

Feedback:


Modified 19.11.18Year 5 Unit 1

Assessment task — Solving simple multiplication, division and fraction problems

Name Class

Part A: Multiplication and Division

1. Calculate the following:

1. a) 240 x 5 = ________

2. Show your working:

3. b) 450 ÷ 5 = ________


5. c) 5463 ÷ 9 = ________


7.

8.

9.

10.

11.

12.

13.

14.

15.

16.


3. (a) Estimate the value of these expressions:

(i) 48 x 12 ___________

(ii) 4805 ÷ 6 ___________

(iii) 440 x 2 ___________

(iv) 1600 ÷ 20 ___________

b) Which of these expressions has a value that is closest to 800? ___________

c) Explain how you solved the problem.

____________________________________________________________________________________________

____________________________________________________________________________________________

____________________________________________________________________________________________

2. Jane thinks that 14 X 98 will give an answer between 1200 and 1500. Explain why her estimate is reasonable?

7.


4. There are 123 students in Jamie’s school.

1. There are between 21 and 26 students in each class.

2. How many classes are there in Jamie’s school?

3. 3 4 5 6

Show how you solved the problem.

5. Stephanie sold 148 boxes of cherries. Each box sells for $22.

5a) Estimate how much money she would make. _______________________

Show your working

5b) Stephanie estimated that she would make about $2200 from sales.

Is this a reasonable estimate? _______________ Why/why not?

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

6. Stephanie bought 264 boxes of mangoes.

She wants to distribute them evenly among her 3 fruit stores.

How many boxes of mangoes will each store receive?

Show your working:

Year 5 Mathematics: Unit 1 — Solving simple multiplication and division problems Name:

Purpose of assessment: To solve multiplication and division problems by efficiently and accurately applying a range of strategies, checking the reasonableness of answers using estimation and rounding.

Understanding and fluency Problem solving and reasoning

Perform calculations using a range of operations.Check the reasonableness of answers using estimation and rounding.

Solve simple problems and verify reasonableness of answers.Explain problem solving processes.

Calculates using multiplication and division in a complex unfamiliar situation. 4 Explains problem solving processes clearly and concisely, using words, jottings, diagrams and/or symbols. 4

A

Correctly estimates the value of all expressions. 3a (ii)Performs calculations using division. 1c

Adapts calculation methods to suit contexts. 1cSolves problems and explains problem solving processes. 4Explains why an estimate is unreasonable. 5b

B

Performs calculations using multiplication and division. 1a, b, 6Correctly estimates the value of expressions. 3a (i, iii, iv), bCheck the reasonableness of answers using estimation and rounding. 2, 5a

Solves simple problems and verifies reasonableness of answers. 1 a, b, 7Explain problem solving processes. 3c, 6

C

Writes answers using multiplication or division. 1a, b, cEstimates the value of an expression. 2, 3a, b

Calculates a correct answer. 1Writes an explanation. 2, 3

D

Represents multiplication and division strategies. 1 Writes an answer to a problem. 2 E

Feedback:


Part B: Fractions


1. Mark and write the fractions 15

110

12 on the number line.

2. Circle the fraction that is greatest:

18 58 38 48

3. a) Circle the fraction that is least.

15 1

10 112 1

7 13

b) Explain your thinking:

9.

4. Using benchmarks show where 14 belongs on this number line?

4. 5. Calculate the following and explain how you reached your answers.

5. 35+ 15=¿

6. 56−26=¿

8. This shape was made using 20 tiles.

8.

(a) What fraction of the tiles is black? ____________

(b) What is the equivalent unit fraction? ___________

(c) Explain your thinking.


6. The following number line represents thirds.

10.Zero and 1/3 are marked. Locate and mark the position of the number ‘one’ on the following number line.

7. Katie made two batches of scones.

11.She added ¼ cup of sugar to a batch and ⅓ cup of sugar to the other.

12.In total, how much sugar did she use?

More than ½ cup of sugar

Less than ½ cup of sugar

More than 1 cup of sugar

Less than 0 cups of sugar

Explain your thinking.

Year 5 Mathematics: Unit 1 — Solving fraction problems Name:

Purpose of assessment: To locate, represent, compare and order fractions and add and subtract fractions with the same denominator.

Understanding and fluency Problem solving and reasoning

Order unit fractions and locate them on a number line. Explain problem solving processes.

Compares the value of two or more fractions. 7 Explains problem solving processes clearly and concisely, using words, jottings, diagrams and/or symbols. 7

A

Identifies a unit fraction from a diagram. 8b Explains identification of a unit fraction. 8c B

Orders unit fractions and whole numbers and locates them on a number line. 1, 4, 6Identifies the greatest and least fractional amounts. 2, 3aAdds and subtracts fractions with the same denominator. 5Identifies the fraction, given the whole. 8a

Explains the value of a unit fraction. 3bExplains problem solving processes. 5

C

Attempts to add or subtract fractions. 5Locates and names a fraction on a number line. 1 Writes an explanation. 3 D

Reads and writes a fraction between 0 and 1. 1 Writes an answer to a problem. 4 E

Feedback:

17.


Year 5 Unit 1 Assessment task — Investigating chance experiments

Name Date

Task

During semester 1, students complete two Mathematical guided inquiries. They are:

Investigating a chance experiment. ‘Is the three-player version of rock paper scissors fair?’ (Unit 1) which focuses on learning related to the sub-strand Chance

Investigating data and constructing data displays. ‘Do most students prefer nutritional breakfast cereals? (Unit 2) which focuses on learning related to the sub-strand Data representation and interpretation.

As a monitoring task observe:

Mathematical guided inquiry

Link to relevant section of the Achievement standard

Quality of student learning:

Is the three-player version of rock paper scissors fair?

Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1.Students pose questions to gather data, and construct data displays appropriate for the data.

Collect evidence that the student can:

identify all possible outcomes of chance experiments

identify equally likely outcomes

assign numerical values (from 0 to 1) to represent probabilities

represent probabilities of outcomes using fractions

classify and present raw data

use data to construct column graphs, dot plots or tables

justify their answer as to whether the game is fair.


The two Mathematical guided inquiries identified can be used as tools to monitor or assess student understanding of Semester 1 work.

Schools can choose to either:

• use both inquiries as assessment • choose to use one inquiry for monitoring and one for assessment,

or• use both inquiries as monitoring tasks.

As an assessment task, the inquiry and the attached Guide to making judgments can be used to report student learning (in line with the Achievement standard) to parents. The specific aspects of the Achievement standard are:

• list outcomes of chance experiments with equally likely outcomes.

• assign probabilities between 0 and 1.


Year 5 Mathematics: Unit 1 — Investigating chance experiments Name:

Purpose of assessment: To use simple strategies to reason and solve chance inquiry questions.

Understanding and Fluency Problem-solving and Reasoning

List outcomes of chance experiments with equally likely outcomes and assigns probabilities between 0 and 1.Connect and apply chance understanding to the inquiry question.

Use mathematical language and symbols.

Interpret, model and investigate chance experiments.Explain and justify conclusions using mathematical evidence.

Accurately transfers knowledge of chance to a three-player version of rock paper scissors.Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Develops and applies methods to gather relevant evidence for a viable solution to a three-player rock, paper, scissors game.Represents and presents evidence logically.Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

A

Recalls and uses appropriate chances experiment understanding connected to the inquiry question.Consistently uses appropriate mathematical language, materials and diagrams.

Develops a method to gather evidence to support a solution to a three-player rock, paper, scissors game.Explains mathematical thinking including choices made, strategies used and conclusions reached.

B

Uses and applies chance understanding to calculate probability of rock, paper, scissors in a game.Uses appropriate mathematical language, materials and diagrams.

Chooses a known method to gather evidence to support a solution to a three-player rock, paper, scissors game.Represents and presents evidence.Describes mathematical thinking including strategies used and conclusions reached.

C

Finds probability of a chance experiment.Uses aspects of mathematical language, materials or diagrams.

Follows a given method to gather evidence.Makes statements about choices or strategies used when prompted. D

Recognises a chance experiment.Uses everyday language. Makes isolated statements. E

Feedback:


MathematicsMonitoring task — Finding the area of rectangles Year 5 Unit 1

Teacher information


[Students] use appropriate units of measurement for length, area, volume, capacity and mass.

[Students] calculate perimeter and area of rectangles.

Materials:

a copy of the task sheet for each student

Task 1:Look for evidence that the student:

• chooses an appropriate unit of measurement• finds the area of rectangles.


Name Date

1. a) Draw shapes on the grid with the following dimensions:

Width Length Width Length

1. 3 cm 5 cm 3. 4 cm 7 cm

2. 2 cm 2 cm 4. 3 cm 3 cm

b) Mark the dimensions on each shape (length and width).

c) Calculate the area and write the answer in square centimetres inside each shape (sq cm).

Mathematics34 of 57Mth_Y04_U1_AT_MathGuidedInquiries

Monitoring task — Finding the perimeter of rectangles Year 5 Unit 1

Teacher information


[Students] use appropriate units of measurement for length, area, volume, capacity and mass.[Students] calculate perimeter and area of rectangles.

Materials:a copy of the task sheet for each student

pencils

Task:Look for evidence that the student:

• chooses appropriate units of measurement for length• calculates the perimeter of rectangles using familiar metric units.


Name Date

Calculate the perimeter of these shapes.

a)

b)

c)

d)

e)

MathematicsMonitoring task — Converting between 12- and 24- Year 5 Unit 1


hour time

Teacher information


[Students] convert between 12- and 24-hour time.

Materials:a copy of the task sheet for each studentdigital and analogue clocksconversion chart from the lessons

Task:Look for evidence that the student:

• represents time on an analogue clock

• converts to digital time and represents on a clock

• converts to 24-hour time and represents on a clock.


Name Date

Draw the hands on the analogue clock and write the digits on the 12- and 24-hour digital clocks to show the times.

Time 12-hour timeanalogue clock

12-hour timedigital clock

24-hour timedigital clock

4pm

A quarter to six in the morning

Quarter past ten at night

2:30 am

10 to 5in the

afternoon


Australian Curriculum

Foundation to 6 Maths - Year 4

Year 5 Achievement StandardBy the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They identify and explain strategies for finding unknown quantities in number sentences involving the four operations. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students interpret different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12- and 24-hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.

Content Descriptions

Number and Algebra Measurement and Geometry Statistics and Probability

Number and place value

Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Fractions and decimals

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

Using units of measurement

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

Calculate perimeter and area of rectangles using familiar metric units (ACMMG109)

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

Chance

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Data representation and interpretation

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

Describe and interpret different data sets in context (ACMSP120)

Curriculum Priorities - Pedagogy

Considerations

Prior and future curriculumRelevant prior curriculum

Students require prior experience with: choosing appropriate strategies for calculations involving multiplication and division recognising common equivalent fractions in familiar contexts making connections between fraction and decimal notations up to two decimal places comparing areas of regular and irregular shapes using informal units solving problems involving time duration identifying dependent and independent events describing different methods for data collection and representation recalling multiplication facts to 10 x 10 and related division facts locating familiar fractions on a number line using scaled instruments to measure temperature, lengths, shapes and objects converting between units of time listing the probabilities of everyday events constructing data displays from given or collected data. describing number patterns resulting from multiplication describing different methods for data collection and representation and evaluating their effectiveness constructing displays from given or collected data.

Curriculum working towardsThe teaching and learning in this unit work towards the following:

solving simple problems involving the four operations using a range of strategies checking the reasonableness of answers using estimation and rounding identifying and describing factors and multiples comparing and interpreting different data sets ordering unit fractions and locating them on number lines ordering decimals and unit fractions and locating them on number lines adding and subtracting fractions with the same denominator using appropriate units of measurement for length, area, volume, capacity and mass calculating perimeter and area of rectangles

Curriculum Priorities - Pedagogy

Considerations converting between 12- and 24-hour time listing outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1 posing questions to gather data, and construct data displays appropriate for the data.

Cross-curriculum prioritiesAboriginal and Torres Strait Islander histories and culturesThe embedding of Aboriginal peoples’ and Torres Strait Islander peoples’ histories and cultures into the curriculum can be a challenging task. For further information, including pedagogical approaches, refer to C2C: Aboriginal peoples & Torres Strait Islander peoples Cross Curriculum Priority support https://oneportal.deta.qld.gov.au/EducationDelivery/Stateschooling/schoolcurriculum/Curriculumintotheclassroom/Pages/C2CAandTSICCPSupport.aspx.

For access to model lessons to address Aboriginal and Torres Strait Islander histories and cultures visit the website YDM-CCP teacher resources (QUT) http://ydc.qut.edu.au/resources/YDM-CCP-teacher-resources.jsp

Username: CCPYDM Password: Curriculum#1

AssessmentAssessing student learning

Assessment name: Interpreting data and posing questions to collect dataAssessment description: Students classify and interpret data and pose questions to gather data.

Assessment name: Solving simple multiplication, division and fraction problemsAssessment description: Students solve multiplication and division problems by efficiently and accurately applying a range of strategies, checking the reasonableness of answers using estimation and rounding. Students locate, represent, compare and order fractions and add and subtract fractions with the same denominator.

Assessment name: Investigating chance experimentsAssessment description: Students use simple strategies to reason and solve chance inquiry questions.

In this unit, assessment of student learning aligns to the following components of the achievement standard.By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They identify and explain strategies for finding unknown quantities in number sentences involving the four operations. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students interpret different data sets.Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12- and 24-hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.

Monitoring student learningStudent learning should be monitored throughout the teaching and learning process to determine student progress and learning needs.Each lesson provides opportunities to gather evidence about how students are progressing and what they need to learn next.Specific monitoring opportunities in this unit may include observation, consultation and samples of student work. For example:

identify factors and multiples fluently recall multiplication facts recall division facts show informal recordings of solutions to multiplication problems represent and order unit fractions using materials and diagrams including number lines order and place unit fractions on number lines solve word problems involving the addition and subtraction of fractions with like denominators model hundredths informally measure perimeters of rectangles using informal units estimate and calculate the perimeter of rectangles estimate and calculate the area of rectangles read and show digital and analog times identify am and pm times and convert to 24-hour time relate whole hours in 24-hour time to am or pm times use a mathematical process to gather evidence and data to answer an inquiry question.

Monitoring task

Monitoring name: Finding the area of rectanglesMonitoring description: Students will be required to choose appropriate units and find the area of rectangles.

Monitoring name: Finding the perimeter of rectanglesMonitoring description: Students will be required to choose appropriate units and find the perimeter of rectangles.Monitoring name: Converting between 12- and 24-hour timeMonitoring description: Students will be required to convert between 12- and 24-hour time.

Year 5 Semester 1 Term 1 Mathematics Report Card Comment BankAssessment Task 1: Interpreting data and posing questions to collect data

A B C D E1M5A1 1M5B1 1M5C1 1M5D1 1M5E1

Interpreting data and posing questions to collect data

{Name} wrote comparative statements using data from a dot plot. {She,He} posed questions to gather categorical data and numerical data for different groups of people.


{Name} interpreted complex data in a frequency table. {She,He} wrote a comparative statement using data from a dot plot. {Name} constructed an appropriate data display, accurately applying graphing conventions. {She,He} explained choice of data representation by referring to features of chosen graph. {Name} posed questions to gather numerical data and categorical data.


{Name} interpreted data in a frequency table. {She,He} wrote a statement using data from a dot plot and constructed an appropriate data display. {Name} classified questions as collecting numerical or categorical data and explained conclusions using data in a frequency table. {She,He} explained choice of data representation and posed questions to collect data about groups of people.


{Name} interpreted some data in a frequency table. {She,He} classified some questions as collecting numerical or categorical data. {Name} posed a question about a group of people.


{Name} answered a question about data. {She,He} posed a question that asked for information.

Assessment Task 2: Investigating chance experiments

A B C D E1M5A2 1M5B2 1M5C2 1M5D2 1M5E2

Investigating chance experiments

{Name} accurately transferred knowledge of chance to a three-player version of rock paper scissors. {She,He} consistently and clearly used appropriate mathematical language, materials and diagrams. {Name} developed and applied methods to gather relevant evidence for a viable solution to a three-player rock, paper, scissors game. {She,He} represented and presented evidence logically. {Name} clearly explained mathematical thinking including choices made, strategies used and conclusions reached.


{Name} recalled and used appropriate chances experiment understanding connected to the inquiry question. {She,He} consistently used appropriate mathematical language, materials and diagrams. {Name} developed a method to gather evidence to support a solution to a three-player rock, paper, scissors game. {She,He} explained mathematical thinking including choices made, strategies used and conclusions reached.


{Name} used and applied chance understanding to calculate probability of rock, paper, scissors in a game. {She,He} used appropriate mathematical language, materials and diagrams. {Name} chose a known method to gather evidence to support a solution to a three-player rock, paper, scissors game. {She,He} represented and presented evidence. {Name} described mathematical thinking including strategies used and conclusions reached.


{Name} found probability of a chance experiment. {She,He} used aspects of mathematical language, materials or diagrams. {Name} followed a given method to gather evidence. {She,He} made statements about choices or strategies used when prompted.


With assistance, {Name} recognised a chance experiment. {She,He} used everyday language and made isolated statements about the experiment.

Assessment Task 3: Solving fraction problemsA B C D E

1M5A3 1M5B3 1M5C3 1M5D3 1M5E3Solving fraction problems

{Name} compared the value of two or more fractions. {She,He} explained problem solving processes clearly and concisely, using words, jottings, diagrams and or symbols.

Solving fraction problems

{Name} identified a unit fraction from a diagram. {She,He} explained the identification of a unit fraction.


{Name} ordered unit fractions and whole numbers and located them on a number line. {She,He} identified the greatest and least fractional amounts and added and subtracted fractions with the same denominator. {Name} identified the fraction, given the whole. {She,He} explained the value of a unit fraction. {Name} explained problem solving processes.


{Name} attempted to add or subtract fractions. {She,He} located and named a fraction on a number line. {Name} wrote an explanation.


{Name} read and wrote a fraction between 0 and 1. {She,He} wrote an answer to a problem.

Assessment Task 4: Solving simple multiplication and division problemsA B C D E

1M5A4 1M5B4 1M5C4 1M5D4 1M5E4Solving simple multiplication and division problems

{Name} calculated using multiplication and division in a complex unfamiliar situation. {She,He} explained problem solving processes clearly and concisely, using words, jottings, diagrams and/or symbols.

Solving simple multiplication and division problems

{Name} correctly estimated the value of all expressions. {She,He} performed calculations using division. {Name} adapted calculation methods to suit contexts. {She,He} solved problems and explained problem solving processes. {Name} explained why an estimate is unreasonable.


{Name} performed calculations using multiplication and division.{She,He} correctly estimated the value of expressions {Name} checked the reasonableness of answers using estimation and rounding. {She,He} solved simple problems and verifies reasonableness of answers. {Name} explained problem solving processes.


{Name} wrote answers using multiplication or division. {She,He} estimated the value of an expression. {Name} calculated a correct answer and wrote an explanation.


{Name} represented multiplication and division strategies. {She,He} wrote an answer to a problem.

Maths Pre-ModerationYear 5: Unit 1 Semester 1 Term 1 Title:

Curriculum Intent for the Unit (see unit /task description) In this unit students apply a variety of mathematical concepts in real-life, lifelike and purely mathematical situations.

Through the proficiency strands - understanding, fluency, problem-solving and reasoning - students have opportunities to develop understandings of:

Number and place value - make connections between factors and multiples, identify numbers that have 2, 3, 5 or 10 as factors, represent multiplication using the split and compensate strategy, choose appropriate procedures to represent the split and compensate strategy of multiplication, use a written strategy for addition and subtraction, round and estimate to check the reasonableness of answers, explore mental computation strategies for division, solve problems using mental computation strategies and informal recording methods, compare and evaluate strategies that are appropriate to different problems, make generalisations.

Fractions and decimals - use models to represent fractions, count on and count back using unit fractions, identify and compare unit fractions using a range of representations and solve problems using unit fractions. Add and subtract simple fractions with the same denominator.

Using units of measurement - investigate time concepts and the measurement of time, read and represent 24-hour time, measure dimensions, estimate and measure the perimeters of rectangles, investigate metric units of area measurement, estimate and calculate area of rectangles.

Chance - identify and describe possible outcomes, describe equally likely outcomes, represent probabilities of outcomes using fractions, conduct a chance experiment and apply understandings of probability and data collection to investigate the fairness of a game.

Data representation and interpretation - build an understanding of data, develop the skill of defining numerical and categorical data, generate sample questions, explain why data is either numerical or categorical, develop an understanding of why data is collected, choose appropriate methods to record data, interpret data, generalise by composing summary statements about data

Assessable Content (Must Know) (Refer to AAP or Unit Plan to source this Information)

Assessment Task 1: Interpreting data and posing questions to collect dataUnderstanding Fluency Classify and interpret data. Construct appropriate data displays.

Problem Solving and Reasoning Pose questions about data in context.

Assessment Task 2: Investigating chance experimentsUnderstanding Fluency List outcomes of chance experiments with equally likely outcomes and assigns probabilities

between 0 and 1. Connect and apply chance understanding to the inquiry question. Use mathematical language and symbols.

Problem Solving and Reasoning Interpret, model and investigate chance experiments. Explain and justify conclusions using mathematical evidence.

Assessment Task 3: Solving fraction problemsUnderstanding Fluency Order unit fractions and locate them on a number line.

Problem Solving and Reasoning Explain problem solving processes.Assessment Task 4: Solving simple multiplication and division problems

Scan and Assess

Prioritise

Develop and Plan

Understanding FluencyPerform calculations using a range of operations. Check the reasonableness of answers using estimation and rounding.

Problem Solving and Reasoning Solve simple problems and verify reasonableness of answers. Explain problem solving processes.

Additional Targeted Teaching Priorities* Identified from previous assessment & post moderation of Semester 1 Mathematics unit. Were there any literacy / numeracy identified areas?

Feedback Guide/Assessment OpportunitiesSee Feedback that may relate to misunderstandings and commo alternative conceptions (in planning – Pre Moderating)Feedback in this unit this may include:

understanding of factors and multiples mental strategies for calculating multiplication and division fraction models data representations (such as tables and graphs) what each student already knows and can do how each student is going where each student needs to go next.

Unit Success Criteria and DifferentiationHow will you know you students have succeeded?

Differentiation: CONTENT PROCESS PRODUCT

and ENVIRONMENT

‘C’ Year Level Achievement Standard – Success Criteria(Refer to GTMJ and relevant content descriptors (AAP) – including prior content – previous levels)

Assessment Task 1: Interpreting data and posing questions to collect data Understanding Fluency Interprets data in a frequency table. Interprets data and writes a statement using data from a dot plot. Constructs an appropriate data display. Classifies questions as collecting numerical or categorical data.

Problem Solving and Reasoning Explains conclusions using data in a frequency table. Explains choice of data representation Poses questions to collect data about groups of people.

Assessment Task 2: Investigating chance experimentsUnderstanding Fluency Uses and applies chance understanding to calculate probability of rock, paper, scissors in a game. Uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Chooses a known method to gather evidence to support a solution to a three-player rock, paper, scissors game. Represents and presents evidence. Describes mathematical thinking including strategies used and conclusions reached.

Assessment Task 3: Solving fraction problemsUnderstanding Fluency Orders unit fractions and whole numbers and locates them on a number line. Identifies the greatest and least fractional amounts. Adds and subtracts fractions with the same denominator. Identifies the fraction, given the whole.

Problem Solving and Reasoning Explains the value of a unit fraction. Explains problem solving processes.

Assessment Task 4: Solving simple multiplication and division problemsUnderstanding Fluency Performs calculations using multiplication and division. Correctly estimates the value of expressions. Check the reasonableness of answers using estimation and rounding

Problem Solving and Reasoning Solves simple problems and verifies reasonableness of answers. Explain problem solving processes.

‘B’ Standard – Success Criteria(Refer to GTMJ and relevant content descriptors)

Assessment Task 1: Interpreting data and posing questions to collect data Understanding Fluency Interprets complex data in a frequency table. 2b Writes a comparative statement using data from a dot plot. 3c Constructs an appropriate data display, accurately applying graphing conventions

Problem Solving and Reasoning Explains choice of data representation by referring to features of chosen graph. 4c Poses questions to gather numerical data and categorical data

Assessment Task 2: Investigating chance experimentsUnderstanding Fluency Recalls and uses appropriate chances experiment understanding connected to the inquiry question. Consistently uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Develops a method to gather evidence to support a solution to a three-player rock, paper, scissors game. Explains mathematical thinking including choices made, strategies used and conclusions reached.

Assessment Task 3: Solving fraction problemsUnderstanding Fluency Identifies a unit fraction from a diagram

Problem Solving and Reasoning Explains identification of a unit fraction.

Assessment Task 4: Solving simple multiplication and division problemsUnderstanding Fluency Correctly estimates the value of all expressions. Performs calculations using division.

Problem Solving and Reasoning Adapts calculation methods to suit contexts. Solves problems and explains problem solving processes. Explains why an estimate is unreasonable.

‘A’ Standard – Success Criteria(Refer to GTMJ and relevant content descriptors + above)

Assessment Task 1: Interpreting data and posing questions to collect data Understanding Fluency Writes comparative statements using data from a dot plot.

Problem Solving and Reasoning Poses questions to gather categorical data and numerical data for different groups of people. 6b Creates a new set of data to match a given column graph and writes a summary statement.

Assessment Task 2: Investigating chance experiments

Understanding Fluency Accurately transfers knowledge of chance to a three-player version of rock paper scissors. Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Develops and applies methods to gather relevant evidence for a viable solution to a three-player rock, paper, scissors game. Represents and presents evidence logically. Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

Assessment Task 3: Solving fraction problemsUnderstanding Fluency Compares the value of two or more fractions.

Problem Solving and Reasoning Explains problem solving processes clearly and concisely, using words, jottings, diagrams and/or symbols.

Assessment Task 4: Solving simple multiplication and division problemsUnderstanding Fluency Calculates using multiplication and division in a complex unfamiliar situation.

Problem Solving and Reasoning Explains problem solving processes clearly and concisely, using words, jottings, diagrams and/or symbols.

Support Plan or ICP Adjusted Content – Refer to ICPStudents:

Tasks: Supported Plan or ICPs Differentiated Assessment

Reporting Sentence: ‘Students working at Year x as per their Support Plan or ICP Plan Tasks and assessments.’

Maker Model Guiding Questions

Content What students need to learn (Select focus questions as required) Can I choose a familiar context to help make

connections or will I scaffold to broaden student world knowledge?

What links can I make to real life? Can I change the context to match student

interests? What prior learning experiences are required? How will I know what students already know?

Which data? Will students complete a Pre-test? Can I skim over some of the content or miss it

completely? How will I extend those students who already

have this knowledge? Will I accelerate students?

Process How students learn (Select focus questions as required) Can I tier the activities around concepts and skills

to provide different levels of support or opportunities to demonstrate deeper knowledge?

Do I need to vary the length of time students require to grasp a concept either by compacting the curriculum or extending the timeframe?

Can I provide opportunities for students to construct and demonstrate knowledge using digital resources and technologies?

Can I scaffold activities or break larger tasks down into smaller tasks?

Can I provide study guides or graphic organisers for targeted students?

Can I modify delivery modes for individuals or small groups?

Can I use peer tutoring?ProductHow students demonstrate what they know (Select focus questions as required) To complete the scheduled assessment task will

some students require more/less time? Can students be extended by communicating the

information in a more challenging way? E.g. change to authentic audience

Are there students who need the assessment task to be broken down for them?

Will some students need adjustments to the task e.g. having concrete materials at hand or access to digital technologies?

Will some students need feedback provided more frequently or in a different manner?

Environment How learning is structured (Select focus questions as required) Which of a range of flexible groupings: whole class, small group and individual, best suits this concept and skill set?Have I offered a range of materials and resources -including ICT's to reflect student diversity?Can I vary the level of class teacher support for some students?Would activities outside the classroom best suit this concept? E.g. Other learning spaces within the school, excursions, campsWhat routines can I put into place to assist students in developing independent and group work skills?What class structures can be modified e.g. team teaching or shared teaching and timetabling?Are there additional support provisions from specialist, teacher aide, mentor etc.?Can I provide visual cues for students e.g. content posters or list of instructions for students to follow?

Feedback: Evidence of Learning

Teaching Sequence Feedback

Lesson 1

Exploring multiples of whole numbersExample learning sequence

Establish learning context Investigate multiples of 2, 3, 5 and 10 Identify common multiples

Evidence of learningCan the student:

Record multiples of 2, 3, 5 and 10? Identify common multiples? Explain the relationship between a number

and its multiples?

Lesson 2Exploring factors of whole numbersExample learning sequence

Establish learning context Investigate factors of numbers to 100 Explore divisibility rules for 2, 3, 5 and 10


Use a range of strategies to identify all the factors of given numbers?

Identify common factors?

Lesson 3Using rounding and estimating of whole numbersExample learning sequence

Establish learning context Practise multiplication and division facts Explore estimation and rounding of whole

numbers Apply rounding to estimate answers


Round numbers to the nearest ten or hundred?

Apply rounding to estimate answers to calculations?

Recall multiplication and division facts?

Lesson 4Using the split strategy to multiplyExample learning sequence

Establish learning context Apply a specific strategy to solve multiplication


Communicate how to apply the split strategy to solve multiplication problems?

Lesson 5Using the compensate strategy to multiplyExample learning sequence

Establish learning context Apply a specific strategy to solve multiplication Apply a strategy to solve multiplication

problems


Communicate how to apply the compensate strategy to solve multiplication and division problems?

Reflect on strategies used to select the more efficient and effective method?

Lesson 6Using a written strategy for addition and subtractionExample learning sequence

Establish learning context Apply the left to right place value method to

solve addition Apply the left to right place value method to

solve subtraction


Apply the left to right written method to solve problems?

Teaching Sequence FeedbackLesson 7Using region models to problem solveExample learning sequence

Establish learning context Compare unit fractions using region models Order sets of unit fractions


Identify the larger or smaller of a pair of fractions, justifying their selection?

Compare region models and reason why one model represents a fraction that is greater than or less than another fraction?

Lesson 20Exploring rounding and estimating with whole numbersExample learning sequence

Establish learning context Consolidate division facts Explore estimation and rounding


Recall the answers to multiplication and related division facts?

Apply rounding to estimate answers to calculations?

Lesson 21Using the split strategy to divideExample learning sequence

Establish learning context Apply a specific strategy to solve division


Articulate how to apply split strategy to solve division problems?

Lesson 22Using the compensate strategy to divideExample learning sequence

Establish learning context Apply a specific strategy to divide


Articulate how to apply compensate strategy to solve division problems?

Lesson 8Investigating unit fractions of a collectionExample learning sequence

Establish learning context Identify unit fractions of collections Compare unit fractions of a collection Solve word problems involving unit fractions


Determine a unit fraction of a collection? Recognise that by determining a unit fraction

of a collection other fractional amounts can be calculated?

Lesson 9Comparing and ordering unit fractions using a number lineExample learning sequence

Establish learning context Identify a unit fraction on a structured number line Locate 1 on a structured number line

Apply benchmarks 0, 1-half and 1 to compare and order fractions


Identify unit fractions on a number line? Order fractions using benchmarks on a number

line?

Lesson 10Comparing and ordering unit fractionsExample learning sequence

Establish learning context Identify and order fractions Apply benchmarks 0, 1-tenth, 1-half and 1 to

compare and order a fraction Count unit fractions


Recognise the distance between zero and one as a unit?

Identify that a unit can be subdivided into fractional parts?


Lesson 11Investigating fractions greater than oneExample learning sequence

Establish learning context Order and compare fractions on a number line Identify and model numbers greater than one

but less than two


Locate and describe a whole as 2-halves, 3-thirds, 4-fourths and so on?

Count on by a unit fraction beyond one? Identify and name fractions that are a unit

fraction greater than one?

Lesson 23

Adding fractionsExample learning sequence

Establish learning context Compare and order common unit fractions Count on and count back using fractions Add fractions with the same denominator Compare fractions in problem situations Add fractions in problem situations


Identify larger or smaller fractions using benchmark fractions?

Solve addition problems that involve concepts relating to unit fractions?

Model adding fractions using number lines and diagrams?

Lesson 24

Subtracting fractionsExample learning sequence

Establish learning context Compare and order common unit fractions Count on and count back using fractions Subtract fractions with the same denominator Subtract fractions in problem situations


Solve subtraction problems that involve concepts relating to unit fractions?

Model subtracting fractions using number lines and diagrams?

Lesson 25

Assessing student learningExample assessment sequence

Understand the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purpose To solve multiplication and division problems

by efficiently and accurately applying a range of strategies, checking the reasonableness of answers using estimation and rounding.

To locate, represent, compare and order fractions and add and subtract fractions with the same denominator.

Lesson 12

Defining dataExample learning sequence

Establish learning context Investigate different types of data Distinguish between numerical and categorical

data and Collect data


Explain the intent of data? Classify data as categorical or numerical? Identify and organise data?

Lesson 13

Interpreting and creating column graphsExample learning sequence

Establish learning context Link questions posed to data types Interpret column graphs Present data in column graphs


Locate data within column graphs to answer questions?

Present data as a column graph and draw conclusions from the data?

Interpret column graphs?


Lesson 14 Evidence of learning

Interpreting and creating dot plotsExample learning sequence

Establish learning context Interpret dot plots Present data in dot plots

Can the student: Locate data within dot plots? Present data as a dot plot according to

recognised conventions and draw conclusions from the presented data?

Pose questions to clarify and interpret information?

Lesson 15

Presenting data using digital technologiesExample learning sequence

Establish learning context Create frequency tables using digital

technology Create column graphs using digital technology Create dot plots using digital technology


Organise data using digital technologies to create tables, column graphs and dot plots?

Generate statements about data presented in dot plots and column graphs?

Manage and operate ICT to present data?

Lesson 16

Assessing student learningExample assessment sequence

Understand the assessment Review the Guide to making judgments and

understand the standards A-E Conduct the assessment

Assessment purposeTo classify and interpret data and pose questions to gather data.

Lesson 17

Identifying outcomes using fractionsExample learning sequence

Establish learning context Describe the probability of outcomes occurring Represent probabilities of outcomes using

fractions


Identify all possible outcomes in chance experiments?

Describe the probability of outcomes occurring using fractions?

Describe chance experiments using the language of chance?

Lesson 18-19

Investigating chance experimentsExample learning sequence

Establish learning context Consider the game (Discover) Review the Mathematical guided inquiry

process (Discover) Prepare to implement (Devise) Develop responses (Develop) Present inquiry responses (Defend) Explore further learning opportunities (Diverge)


Discuss and demonstrate understanding of and reason for chance applications and values in mathematical and authentic contexts?


Lesson 26 Evidence of learningCan the student:

Measuring timeExample learning sequence

Establish learning context Investigate measuring time Identify am and pm times Convert between analog and digital time

Read and show times on analog and digital clocks?

Convert between digital and analog times? Distinguish between am and pm times?

Lesson 27

Investigating 24-hour timeExample learning sequence

Establish learning context Investigate the concept of 24-hour time Convert simple 24-hour time Compare 24-hour time to times of day


Relate whole hours in 24-hour time to am or pm times?

Lesson 28

Reading and representing 24-hour timeExample learning sequence

Establish learning context Explore minutes in 24-hour time Convert between 12- and 24-hour time Measure time (Monitoring task)


Read and represent 24-hour times? Convert am and pm times to 24-hour time?

Lesson 29

Exploring perimeterExample learning sequence

Establish learning context Investigate perimeters of rectangles using

informal units.


Identify the perimeter of closed shapes? Calculate the perimeter of squares and

rectangles using informal units?

Lesson 30

CalculatingPerimeterExample learning sequence

Establish learning context Calculate perimeters of rectangles (Monitoring

task)


Calculate the perimeter of rectangles (including squares) using metric units?

Explain method/s for calculating perimeter?

Lesson 31

Exploring area Example learning sequence

Establish learning context Investigate areas of rectangles)


Identify area as the space inside a closed shape?

Calculate the area of rectangles (including squares) using informal units?

Identify the metric units used to measure area?

Lesson 31

Calculating area Example learning sequence

Establish learning context Calculate areas of rectangles Calculate areas of rectangles (Monitoring task)


Calculate the area of rectangles (including squares) using metric units?

Explain method/s for calculating area?

Post Moderation “Every Student Succeeding”

Objective: Develop professional knowledge and practice (Refer to Pialba state School Moderation and Reporting Policy)

Moderation ProtocolsRefer Appendix of Pialba State School Reporting and Moderation (pre-post) School Policy – Social Moderation Norms.

Moderation of Completed MATHS Assessment Samples Refer Appendix of School Policy – Making judgements using standards.

Previously agreed criteria (Pre Moderation) A-E given using the GTMJ On balance teacher judgement- poles Start at the C Move up or down according to the evidence in the sample. The achievement standard is the C standard. Compare each student sample to the standard not against other student samples Give an A-E grade for the task This sample will become part of the student’s portfolio of work

Where to next after Moderation Refer Appendix of School Policy – Moderation Reflection Tool. From the moderated samples information can then be used to plan for the next task. Complete in next Maths Unit the ADDITIONAL TARGETED TEACHING PRIORITIES

Identified from this terms assessment & moderation as well as the Show Me Tasks.

Scan and Assess

Act

Review

Prioritise

Review

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