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PIALBA STATE SCHOOL: MATHEMATICS YEAR 4 SEMESTER 1 UNIT 1 PLAN

Proficiency Strands

At this Year level:

• understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes

• fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instuments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data

• problem-solving includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns

• reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

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

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

1 D Show Me Term 1 Pre-Test

3 M Understanding place value, fractions and operations

4 M/S Investigating the Nature of 10 000

6 S Recalling and Using Multiplication and Division Facts

8 S Identifying and explaining chance events

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 VALUE4-digit Numbers

#Warm Ups Partition Party Get Closer Four Square Yr 4 Order and Compare PPT

#Number Talks: 2307 + 564 = □ True or False: 6Th + 47T +5 ones = 64H + 6T

+15ones#ActivitiesFour Digit Numbers: Revise place value on 4-digit number

o Use number expanderso represent with MABs on place value matso show with standard and non-standard

partitioning Sheet: Ordering 4-digit Numbers

o Discuss with students strategies to order numbers. i.e. start from the highest place, if it is the same move on to the next etc.

Number Lines:o order 4 digit numbers on a number lineo locate numbers on a number line (using

different number lines) e.g.

Linked to Monitoring Task:

Understanding place value, fractions and

operations

Use some 4-digit numbers that have 0 in one or more

places. Do student recognise and read the numbers and

represent it accurately

Students should be able to recognise benchmarks and

even intervals when locating numbers

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 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 Yr 4 Order and Compare

PPT Sheet: Order 4-digit

Numbers Greater Than, Less Than,

Equal to Crocodile Symbols

Greater than, Less than Mat

Languagebenchmark, partition, compare, standard/non-standard, digit, number, tens of thousands, thousands, hundreds, tens, ones, place value, place holder (0), number line, greater than, less than, equal to, number sentence, strategy, multiplication, divisionWalt: Represent, compare and

order 4-digit numbers

Wilf: Write, read and model 4-

digit numbers. Compare and order 4-digit

numbers

Tib: 4 digit numbers exist in our

daily lives and routines e.g. shopping, labels, weights, location, money

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



Compare 4-digit numberso Use Greater Than, Less Than and Equal To

Crocodile Symbols to compare numbers Where and why do we use 4-digit Numbers in

the real world? (use pictures for hints). Find examples in newspapers etc

#Open-ended How many ways can you partition 1265? I am going to buy a TV that costs $4628. I only

have $100, $10 notes and $1 coins. What combinations of notes and coins could I use?

Students should understand that our maths is used in our

daily lives outside of the classroom and so has a

purpose

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 VALUEInvestigating 10 000

Inquiry Question:‘How much is 10 000?’

# ActivitiesFollow the Mathematical Inquiry Method outlined in the resource Investigating the Nature of 10 000

Establish learning context

Explore number representation (Discover)

Plan how to explore the question (Devise)

Follow plans to collect and review evidence

(Develop)

Explain results and draw conclusions

(Defend)

Explore further learning opportunities

(Diverge)

GUIDED INQUIRYInvestigating the Nature of 10

000

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

C2C Maths Library:https://learningplace.eq.edu.au/cx/resources/file/3ea6ae58-5cb2-4db6-8fd2-43d3563ffe8a/1/Mathematics_Library/index.html

collections of small objects (e.g. pasta shells, nuts, lentils, seashells, dried beans)

transparent container (e.g. glass, jar)

marker pens poster paper

Languageplace value, ‘how much’, ones, tens, hundreds, thousands, number, digit, representation, quantity, estimate, Walt:

Wilf:

Tib:







Check for Understanding

Differentiation Resources

NUMBER AND PLACE VALUE

Addition and Subtraction

#Number TalksFrequent use of number talks will help build efficient strategies 167 + 173 = □ 1000 – 499 = □#ActivitiesRecall Addition Facts Play a variety of warm up games to build fluency

o Coverso Headache o Fifteenso Cross Out Singleso Fives

Recall strategies for number factso use counting — use count on or count back by 1 or 2 (e.g. 4 + 1, 2

+ 7, 9 – 2, 8 – 7)o use five — use knowledge of five as a benchmark

number, including its relative position in relation to ten and tens names (e.g. 5 + 3, 9 + 6, + 5 = 11, 4 + 7 (5 + 7 less 1))

o use doubles — use knowledge of doubles including near doubles (e.g. 8 + 8, 5 + 6, 5 + 7, 12 – 6, 9 – 4)

o use ten — use knowledge of number combinations that make ten or near ten (e.g. 7 + 3, 4 + = 10, 3 + 8 =)AND — use knowledge of adding ten or near ten (e.g. 4 + 10, 17 – = 10, 9 + 6 =)

o use a rule — add or take away zero and the quantity stays the same, or take away all of a collection and the quantity is zero (e.g. 4 + 0, 11 – 0, 9 – = 0).

Learning Object: Doubles and Near DoublesAddition and Subtraction Build fluency in addition and subtraction strategies in 4 digit

numbers (promote THINK, SCAN, DO) – (use MABs and place value beads for those students that are not as confident)o jump strategyo compensate strategyo split strategy

#Open Ended Five numbers added together make an odd numbers. What

Linked to Monitoring Task:

Understanding place value, fractions and

operations

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

C2C Maths Library:


Covers Game board Dice counters whiteboard markers cards whiteboards whiteboard markers MABs Bead strings

Languageaddition, subtraction, add, plus, sum, subtract, take away, minus, strategies, efficient, number facts, digit, place value, fluency,

Walt: use known number

facts to add and subtract 4-digit numbers

Wilf: efficient strategies accurate recall

Tib: Efficient recall of

number facts helps us when adding and subtracting larger numbers




do you know about the numbers?




Check for Understanding Differentiation Resources

NUMBER AND PLACE VALUEMultiplication and Division

2s, 4s, 5s, 10s

#Warm ups Number Fact Relay Triangle Quiz#Number Talks 40 x 8 = □ 53 x 4 = □

#Activities Discuss and model making multiples of set

numbers, e.g.o use your counters to show 3 fives;

examine this array; o Discuss that 15 is a multiple of 3 and 5

recall strategies for remembering 2, 4, 5 and 10 times tables (See Multiplication Strategies Poster)

o Investigate patterns in number facts with a calculator and record what they observe

Build fluency of time tables o Around the world, Buzz, Find Me Games o Times Table Songso Standard times tables rehearsal with

concrete materials Fact Family Triangle s (Multiplication and Division)

this should also be represented in a part, part, whole model so that students are familiar with both

Sheet: (whole class or individual) Multiplication and Division Word Problems (Promote THINK, SCAN, DO)

Write word problems (refer interchangeably as word problems and word stories)

Investigate patterns in multiplication facts

Mulitplying by 10 and 100 Visual representations of what multiplying by 10

Building for Assessment:Recalling and Using Multiplication and

Division Facts

Check to ensure students understand the

commutative principle also applies to multiplication (i.e.

9x5x2 = 2x9x5

When multiplying by multiples of 10 and 100,

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

Multiples of times tables printed, cut out and hanging in different areas (Find Me)

Times Table Songs Materials for making

groups and sharing (MABs, counters, buttons, bundling sticks etc.)

lollies Multiplication strategies

poster Multiplication and Division

Word Problems Place Value Flip Book Learning Object: Number

Slider

Languagemultiple, number facts, multiply, divide, arrays, repeated addition, number sentence, word problem, word story, THINK SCAN DO, Walt: Build fluency and understanding of multiplication and division facts

Wilf: Using efficient strategies

to use multiplication and division in context

Use known multiplication facts to calculate extended facts (x10, x100)

Tib: Having fluency and

strategies with multiplication and division helps us to solve problems efficiently in our everyday lives

looks like (anchor chart) – Use Place Value Flip Books to assist in representing getting 10x larger (also see Learning Object: Number Slider)

Investigate how multiplication and division are related (fact family triangles)

Multiply two-digit numbers by 10 on the calculator. Notice the pattern.

Extended facts – Multiplying and dividing i.e. 3x3, 3x30, 3x300 AND 34 x 10, 34 x 100 etc

Reinforce the concept that place value in numbers uses multiplication and division.

o For example:o 3 640 is 10 times _________________

than 364o The digits in 3 643 are one place to the

_______________ of the digits in the number 364

o 3 640 ÷ 364 =

#Open Ended A number is multiplied by 5. The answer is

greater than 72. What could it be? Prove it.

There are 128 lollies at a party. If each person gets an equal amount, how many do they each get?

students should be able to recognise the related

number fact and use that as an efficient strategy





PATTERNS AND ALGEBRA#Warm ups Mash Up Maths (See PDF Booklet – chose an

appropriate challenge/s) Make it Balance#Number Talks 53 + □ = 102

□ x 10 = 230#Activities Less Than, Greater Than, Equal To

o Explicit Lesson: Less than, greater than, equal to, not equal to – meaning and symbols (use Greater Than Less Than Equal To symbols)

o Learning Object: Sing it! Crocodile Biteso Write number sentences to describe

relationships using correct symbols (<,>,=, ≠)o Use balance scales and concrete materials to

visually reinforce the meaning of equivalence and non-equivalence.

o replace concrete materials with numbers and symbols

o practice verbalising situations (i.e. 10+12 is equal to 8+14)

Finding Unknown Quantities o Problem Solving: Balance Scale Problem PPTo Balance Scale: put an unknown value in a

bag on one side of the scale. Students work together to determine the value using problem solving and reasoning (verbalise their thinking: “I know there must be less than 5 because it is not balanced)

Assessment: Number (Recalling and

Using Multiplication and Division Facts)

Also linked to: Monitoring Task:

Understanding Place Value, Fractions and

Operations

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

Mash Up Maths Booklet Greater Than Less Than

Equal To symbols Greater Than, Less Than

Posters Learning Object: Maths

Sing it! – Crocodile Bites Balance scales and

concrete materials (i.e. marbles, unifix cubes etc. note materials should be uniform in size)

Balance Scale Problem PPT plasticine 50gram and 20 gram

weights

Languageequivalent, balance, less than, greater than, equation, number sentence, unknown, equal to, not equal to, part, whole, difference, inverse relationship, addition, subtraction, multiplication, division Walt: Balance unknown quantities within equations

Wilf: Use the symbols of greater

than, less than or equal to appropriately.

Use strategies to work out unknown quantities

Tib: We need to be able to work out unknown quantities in a variety of real life and everyday situations

o Use balance scales to represent equations where known and unknown values are presented. Students explore strategies to work out the missing value

Be explicit about using the inverse operation to undo and find the unknown

Equations with unknown quantitieso Model (explicitly teach) how to find an

unknown quantity in a written equation using multiple strategies

o Word stories – present word stories with unknown addends

o Extend into multiplication and division#Open Ended Write an equation using two addends on each

side of the equal sign (□ + □ = □ + □)





FRACTIONS AND DECIMALSFractions

#Warm ups “Roll, Slide, Cover” Fractions Game#Number Talks

#Activities Fold paper into halves, quarters and eighths.

o Have student explain why one half is larger than one eighth. Compare and order the fractions from least to most. Fold paper into third, sixths and ninths. Compare and order the fractions from least to most

Provide students with fractions to compare. o i.e. 3/8 and ½. Which is smaller? Prove it.

(Students can draw pictures etc, however, students should be able to explain that 4/8 is half and so 3/8 is less than that.

Compare Fractions: o Use Sheet ‘Ways to Compare Fractions’ as

an idea for an anchor chart to discuss and represent strategies to compare fractions

Show symbolic representations of fractions. o Shade parts of a whole: link to vocabulary of

the denominator showing ‘total number of equal parts’ and the numerator showing ‘number of equal parts to be considered’ and the vinculum separating these numbers

Explicit lesson: o Fold a length of rope in half, quarters and

eighths. Mark each of these folds in the rope. Unfold and explicitly link to being a number line showing fractions. Model a closed number line with 0 and 1 labelled on the ends. Label fractions. Be explicit that 1 is the whole fraction. Develop the idea that the larger the denominator, the smaller the fraction.

Monitoring Task: Understanding place value, fractions and

operations

Do students recognise the relationship between

halves, quarters and eighths (double, double-double, double-double-

double)

Students need to be provided with

opportunities to show reasoning

Do students understand the symbol of fractions?

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

Sheet - Fractions Exit Ticket

‘Roll, Slide, Cover’ Fractions Game

Dice Counters Rope Sticky notes or labels Paper shapes Sheet: Fractions Wall Learning Object: Number

Lines Blank Number Line Sheet sandwiches, apples,

oranges, Ways to Compare Fractions

Language

fraction, half, quarter, third, fifths, sixth, eighth, ninth, tenth, number line, numerator, denominator, vinculum, part, whole, equal, common fraction, improper fraction, mixed fraction

Walt: Compare fractions Locate fractions on a

number line

Wilf: understanding of

numerators and denominators

reasoning to make comparisons between fractions with like and unlike denominators

Tib: We use knowledge of

fractions to solve problems in our daily lives (cooking, shopping, etc)

Fractions Exit Ticket – o complete to check in on students

understanding of the fractions symbols Explore Equivalence with a Fraction Wall –

o ask focus questions to guide students’ understanding of equivalence and parts of a whole (See Blank Fraction Wall Sheet)

Learning Object – Number Lines. o Change Number Line to model common

fraction. Move the arrow to represent the given fraction

Blank Number Line Sheet – o give students different fractions to represent

on the number lines. Repeat activity using 2 to finish the number line

Count physical fractions (sandwiches, apples, oranges etc cut into different fractions). o Count in fractions, i.e. one half, two halves

(if students continue with three halves, four halves, ask them to think about what three halves might be. Represent this counting using improper fractions and discuss explicitly with students)

#Open Ended I have some fish in my aquarium. Half of them are

orange; a quarter of them are blue and the rest are green. What might my fish tank look like?

This chocolate bar has been cut in half. How many ways can you represent half using different fractions?

Check that students recognise when counting,

that two halves are a whole, continue counting

1 ½, 2, 2 ½ etc…





MEASUREMENTTime

#Warm Ups

Stop the Watch (Learning Object – Reaction Time Test): In pairs, students stop the tester as close as possible to 1 second, 10 seconds or 1 minute (time is in milliseconds)

#Activities Brainstorm events that take: seconds, minutes,

hours Explicit Lesson – convert between seconds,

minutes and hours. Use Display Posters as a resource to leave in the classroom

Use clock whiteboards to read and show times to the quarter hour – Learning Object: ‘Clocks – Analogue and Digital’ may be helpful

Stopwatches – Whole class, stop the time as close to a given interval as possible.

Explore minutes past and minutes to the hour on an analogue clock. Practice reading it in different ways (7 thirty-five, 25 to 8, 35 minutes past 6 o’clock)

Explore the 24 hours of a day. Create a timeline to show the 24 hours and list events that might happen at different time. Label am and pm. (See resource – am to pm Timeline

Discuss the meaning of ‘am’ (ante meridiem – before midday) and ‘pm’ (post meridiem – after

Check to see if the student can convert between

seconds, minutes and hours.

Do students have fluency around the minute and hour

hands (i.e. ask how they know that a clock says 5 past 1 and not 1 past 5)

Check that students understand am and pm

times

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

Time Display posters Learning Object: Reaction

Time Test Learning Object: Clocks

Analogue and Digital Sheet: am to pm Timeline Sheet: 24 Hour Time Cycle Clock whiteboards Individual Student clocks Teacher’s Magnetic class

clock Sheet: Calculating with

Analogue and Digital Time

Language

time, units, am/pm, midday, midnight, seconds, minutes, hours, convert, quarter hour, digital, analogue, intervals, past, to,

Walt: Represent time as AM or

PM Read and write time to

minute intervals Calculate the duration of

time

Wilf: Using AM and PM to

represent time of day using strategies to solve

time problems

Tib: We need to understand

how to calculate time duration so we can plan for events in our daily lives

midday) Sheet – 24 Hour Time Cycle Explicit lesson: Calculating Durations (i.e. count

on/back the hours and then the minutes). Model using a number line

Present a range of durations problems for students to solve including: start time and end time given; start time and duration given; duration and end time given. (begin to work with whole hours, half hours and 15 minute intervals. once students have a firm understanding of time calculating, they should be extended to 5 minute and 1 minute intervals)

Sheet – Calculating with Analogue and Digital Time

#Open Ended Charlie rode his bike for 25 minutes. What time

might he have started and finished?





MEASUREMENTLength

#Warm ups Measuring Length Warm Up PPT#Activities Learning Object: Measure it Through History Identify the need for formal units of measure –

i.e. students measure a variety of objects using arm lengths, hand spans, feet etc. Discuss why this is not a completely accurate measure and when this would and would not be appropriate to use.

Identify tools for measuring length with formal units. Use ‘Measuring Length Display Poster’ as a reference

Explicit Lesson: How to use a ruler correctly Use rulers, measuring tapes and trundles to

measure the length of objects, distance between objects and distance around objects.

Focus questions: Which is bigger: 1cm or 1m? How many centimetres on a metre ruler? What things would be best to measure with a classroom ruler/metre ruler/measuring tape/trundle?

#Open Ended What is something in the classroom that is more

than 50cm but less than 1m? Jack is 1m tall, Sarah is 2m tall. Ben’s height is

somewhere in the middle. How tall might he be?

Check that students line up the end of an object to the 0cm mark, and not to the

end of the ruler

Do students identify and read units of measurement

correctly?

Check that students understand the relationship between centimetres and

metres (teach the meaning of the prefix centi-)

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

Learning Object: Measure it Through History

Measuring Length Display Poster

Measuring Length Warm Up PPT

trundles, 30cm and 1m rules, measuring tapes

Languagemarks, measure, metre, centimetre, length, long, high, distance, point, around, formal units, width, girth, tall Walt: Use informal units to measure length

Wilf: Choose appropriate

measurement tools Measure accurately using

formal units (i.e. from the 0cm not the end of the ruler)

understanding that cm are smaller than metres

Tib: Measuring accurately in

formal unit is a skill used by many occupations in the real world





STATISTICS AND PROBABILITYChance

#Warm ups

#Number Talks

#ActivitiesIdentifying the likelihood of events Use the language of chance throughout the day

to describe everyday events o (i.e. When you line up for parade: what

are the chances that we beat every other class to parade? When packing up activities: What are the chances that the blue group will be ready before the red group?)

Create a chance continuum (number line) on the board with magnetic crosses that can be moved and talk to each day.

o i.e. move the cross to unlikely when the class talks about going out to play on a rainy day etc.

Explicit Lesson: o Identify chance language and events to

match Probability Events Matching Cards:

o Use as a whole class (cut and paste under the correct heading) OR laminate and use and rotation activities

o Think/pair/share to justify why you have placed event in a particular place. Share with class and display class justifications

Order Familiar Events Sheet Rolling Dice & Flipping Coins:

o Identify the chances of rolling certain numbers, odd numbers, even numbers;

ASSESSMENT Identifying and

explaining chance event

Check that student think around the events and what might make them

more or less likely

Create a language poster to ensure students understand the language of probability

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

Magnetic crosses (or similar)

Probability Events Matching Cards

Sheet: Order Familiar Events

Sheet: Probability Open-ended Skiing Holiday

Dice coins grab bag spinners

Languageprobability, chance, likely, unlikely, certain, impossible, equal chance, even chance, 50/50, justify, independent events, dependent events, everyday events Walt: Identify and explain

chance events

Wilf: Use language of chance

appropriately and justify my choices.

Identify independent and dependent events

Tib: In everyday life, we need to evaluate and use chance to make informed decisions

or flipping a head or tail. (Students should able to recognise that these all have an equal chance, 50/50, even chance)

Conduct chance experiments: grab bag, flipping coins, rolling dice, spinners etc. Predict and test predictions

Independent and dependent events: Explicit Lesson: Define dependent and

independent events Display a list of dependent and independent

eventso Last month was March. This month is April.o I rolled a six. I rolled a three.o I ate breakfast. I brushed my teeth.o The clock showed 4.15 pm. The clock showed 4.16 pm.o I put on my socks. I put on my shoes.o Dad put the pizza in the oven. The pizza cooked.

Have students: examine each pair of events sort the events according to whether the

occurrence of the second event is dependent or independent in connection to the first event

discuss decisions as a class and justify choices.

#Open Ended Sheet: Probability Open-ended Skiing Holiday In a bag there are some balls. I draw out one ball

and it is red. I put it back and draw again. This time the ball is black. I put it back. After ten draws. I have drawn out three red and seven black. How many balls might there be in the bag and how many might be black?





STATISTICS AND PROBABILITYData Representation

#Activities Identify ‘why’ we need to collect data Brainstorm a variety of questions (relevant to the

classroom or school) that would require data to answer.

Model and discuss ways of collecting data

Identify which method would be most appropriate for class identified questions

Use sheets: ‘What’s your favourite ice-cream flavour?’ and ‘What’s your favourite sport?’o Model how to interpret the data. Why

would the data need to be collected? What can it tell us?

Conduct surveys within the classroom (or school)o collect data in two way tables

Explicit lesson: Displaying data in Picture Graphs and Column Graphs (Display posters can be used as a resource)

Use collected data to create picture graphs and column graphs

Interpret a picture graph:o Sheet: One-too-Many Picture Graphs.

Complete the sheet either as a whole class

Use real world examples of where collecting data is

important so that students see the purpose in the

activity

Check that student understand good questions

to ask to collect relevant data

Can students provide reasoning for why one method of collection is

better than another for a specific question/purpose?

L2B







U2B




Independent Work

Peer Instruction

Tiered tasks

Sheets:o What’s your favourite

ice-cream flavour?o What’s your favourite

sport? Column Graph Display

Poster Pictogram Display Poster Picture Graph Display

Poster Sheet: One-too-Many

Picture Graphs Learning Object: Graph

Maker

Languagedata, collect, frequency table, tally, observation, survey, experiment, research, question, method, conduct, interpret, graph, picture graph, pictograph, column, title, axis, Walt: Collect and represent data

Wilf: Interpret data displays by

using information to provide reasoning

transferring collected data accurately into graphs

Tib: We collect data in the real

world to provide information and plan for events efficiently and effectively

or individually Learning Object: Graph Maker

#Open Ended This is a graph about a grade 4 class. What is it

about? How many children might there be in the class?

Students should be aware that the pictures in

pictographs can represent more than one

Year 4 Unit 1 Assessment task — Investigating the nature of 10 000

Name Date

Task:

During Semester 1, students complete two mathematical guided inquiries. They are:

Investigating the nature of 10 000. ‘How much is 10 000?’ (Unit 1) focuses on learning related to the sub-strand Number and place value

Investigating distance using maps. ‘What is the shortest distance around Australia?’ (Unit 2) focuses on learning related to the sub-strand Location and transformation.

As a monitoring task observe:

Mathematical guided inquiry

Link to relevant section of the Achievement standard

Quality of student learning:

How much is 10 000?

Students choose appropriate strategies for calculations involving multiplication and division. They recall multiplication facts to 10 x 10 and related division facts.

Collect evidence that the student can:

apply place value knowledge

formulate a plan to solve an authentic number problem

explain the thinking they used to solve the problem

justify their answer to the problem with mathematical evidence.

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 aspect of the achievement standard is as follows:

choose appropriate strategies for calculations involving multiplication and division

recall multiplication facts to 10 x 10 and related division facts.

19 of 49Mth_Y04_U1_AT_MathGuidedInquiries

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:

• use both inquiries as assessment

• choose to use one inquiry for monitoring and one for assessment, or

• use both inquiries as monitoring tasks.

Year 4 Mathematics: Unit 1 — Investigating the nature of 10 000 Name:

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

Understanding and Fluency Problem-solving and ReasoningRecognise, represent and order numbers to answer the inquiry question.Apply place value to partition, rearrange and regroup numbers to at least tens of thousands.Use mathematical language and symbols.

Interpret, model and investigate place value and quantity.Explain and justify conclusions using mathematical evidence.

Accurately transfers knowledge of numbers to complex-situations.Consistently and clearly uses appropriate mathematical language, materials and diagrams.

Develops and applies methods to gather relevant evidence for a viable answer to how much is 10 000.Represents and presents evidence logically.Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

A

Recalls and uses appropriate order of number understanding to answer the inquiry question.Consistently uses appropriate mathematical language, materials and diagrams

Develops a method to gather evidence to support answer to how much is 10 000.Explains mathematical thinking including choices made, strategies used and conclusions reached.

B

Recognises, represents and orders numbers to answer the inquiry question.Applies place value to partition, rearrange and regroup numbers to at least tens of thousands.Uses appropriate mathematical language, materials and diagrams.

Chooses a known method to gather evidence to support answer to how much is 10 000.Represents and presents evidence.Describes mathematical thinking including strategies used and conclusions reached.

C

Uses aspects of mathematical language, materials or diagrams.Identifies place value up to tens of thousands.

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

Recognises the number 10 000.Uses everyday language. Makes isolated statements. E

Feedback:

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Modified 19/11/18Year 4 Unit 1

Assessment task — Recalling and using multiplication and division facts

Name Date

1. Write the missing value in the box.

a) 10 × = 20 b) × 8 = 32 c) 35 = 5 x d) 90 ÷ = 9 e) ÷ 4 = 6

2. Write the missing value in the box.

a) 30 × 3 = b) 40 × 5 = c) 80 x 2 = d) 120 ÷ 4 = e) 350÷ 5 =

3. Write the missing value in the box. Show your working out. Use diagrams where needed.

a) 40 x 5 = b) 4 x 3 = x 6 c) 20 ÷ 5 = ÷ 2


4. $160 is shared equally among 4 people.

Write a number sentence or model to find out how much money each person will receive.

a) Number sentence:

b) Show your thinking:

5. Using this fact family triangle write:

a) a multiplication word problem (or situation)

b) a division word problem (or situation)

6. Aidan did 95 push-ups every day for 10 days. He wanted to know his total number of push-ups. Show 2 ways to solve the problem.


40

5 8

Year 4 Mathematics: Unit 1 — Recalling and using multiplication and division facts Name:

Purpose of assessment: To recall multiplication and division facts, identify and explain unknown quantities and solve problems using appropriate strategies for multiplication and division.

Understanding and Fluency Problem-solving and Reasoning

Recall multiplication and division facts. Choose a strategy for multiplication and division. Identify unknown quantities in number sentences. Solve problems and explain thinking and reasoning.

Identifies a missing value in a division number sentence. 3cWrites a division word problem/situation using a given fact family triangle. 5b

Applies and explains strategies relating to number sentences/models. 3b, cClearly explains mathematical thinking to justify strategies to solve a problem in two different ways. 6

A

Recalls multiplication and division facts in non-standard representation. 1a-eIdentifies a missing value in a multiplication number sentence. 3bWrites a multiplication word problem/situation using a fact family triangle. 5a

Applies and explains a strategy relating to a number sentence or model. 3bExplains mathematical thinking to justify strategies to solve a problem. 6 B

Recalls some multiplication/division facts in non-standard representation. 1a-eIdentifies missing values in number sentences about extended facts. 2a-eChoose a strategy for multiplication 3aWrites a number sentence to represent a division word problem. 4aRepresents a multiplication situation or problem. 6

Solves a simple familiar word problem and explains thinking and reasoning. 4b C

Identifies some missing values in number sentences about extended facts. 2Attempts to write a number sentence to represent a word problem. 4a Attempts to solve a simple familiar word problem. 4b D

Writes a number sentence. E

Feedback:


MathematicsMonitoring task — Understanding place value, fractions and operations Year 4 Unit 1

Name Date

Place value

1. Draw lines to match the numbers.

9 503

7 261

1 253 six thousand, nine hundred and thirty-five

6 935 7 000 + 200 + 60 + 1

2. Write the value of ‘8’ in each number below.

8 361 __________________ 2 084 __________________

857 __________________ 7 908 __________________

3. Use the digits 5, 1, 2 and 7 to make the largest and smallest numbers possible.

__________________ ___________________

4. Use the symbols < or > to make the following true.

7 203 7 023 5 150 5 501 1 965 1 956


5. Show the numbers 4 150, 4 500 and 4 401 on the number line below.

6. Use standard and non-standard partitioning to show the number 8 214 in three different ways.

____________________________________

____________________________________

____________________________________

Operations

7. Work out the answers to these problems. Show your working for each problem.

a. 113 + 246 = ________ b. 897 – 295 = ________

c. 516 + 298 = ________ d. 624 – 449 = ________

8. What strategies can you use to help you remember these multiplication facts?

2s facts: 10s facts: 4s facts:


9. Write the set of multiplication and division facts for each of these:

10. Use your multiplication facts and what you know about multiplying by tens or hundredsto solve these:

2 x 4 = ___ 20 x 4 = ____ 2 x 40 = ____ 200 x 4 = _____ 2 x 400 = _____ 20 x 40 = _____

5 x 6 = ___ 50 x 6 = ____ 4 x 40 = ____ 200 x 5 =_____ 7 x 400 = _____ 30 x 50 = _______

Fractions

11. Complete the counting sequences:

a. 1 quarter, 2 quarters, __________________, _________________, ________________.

b.58 , 68 , 78 , c. 1

34 , 1

24 , 1

14 ,

12. Write the missing numbers:

a. 1 whole = ____ halves b. 2 wholes = ______ quarters

c. 2 wholes = ____ eighths d. 3 = _____ halves

13. Partition and then shade the following diagrams to show the fractions:

a. one half b. 24 c.

12 d.

58

14. Circle the bigger fraction in each pair:

12 18

12 34

68 24

32 1 14

78 34

124 2 12

15. Show where these fractions would sit on the number line: 12 3 12

14 1 34 2 48

0 1 2 3 4


24

4 6

45

9 5

Modified 16/11/18Year 4 Unit 1

Assessment task — Identifying and explaining chance events

Name Class

1. Match each of the events to one of the chance words. Write the letter in a box.The first one has been done for you.

A. The sun will rise tomorrow.

B. I will visit the moon next week.

C. A tossed coin will land on tails.

D. I will yawn today.

E. I will have chocolate for dinner tonight.

F. A rolled dice will produce an odd number.

2. a) You roll a regular 6-sided dice. Order these events from least likely to most likely.

a ‘6’ is rolled an odd number is rolled a ‘7’ is rolled

least likely most likely

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equal chance

impossible

likely

certain

A

unlikely

b) Events that occur as a part of our everyday lives are called ‘an everyday event’.Write an example of an everyday event.

_______________________________________________________________________

Draw a cross on a line to show the likelihood of its occurrence.

least likelymost likely

c) Describe the likelihood of your everyday event happening. Justify your placement of the everyday event on the line.

3. Read each pair of statements.

Choose if the events are dependent or independent and explain why.

I get dressed. I have breakfast.

Dependent independent

Explanation:

I turn on the X box. I play the X box.

Dependent independent

Explanation:

4.

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5.

Matt and Laura toss a coin three times.

The tosses produce three (3) tails.

Matt predicts that on the next toss the coin will land on heads.

Laura predicts that on the next toss the coin could land on heads or tails.

a) Who has predicted correctly?

b) Justify your choice of which person is correct.

c) List all possible outcomes for the next two coin tosses.

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a) Write two independent events. b) Write two dependent events.

Year 4 Mathematics: Unit 1 — Identifying and explaining chance events Name:

Purpose of assessment: To identify dependent and independent events and explain the chance of everyday events occurring.

Understanding and Fluency Problem-solving and Reasoning

List and compare everyday events according to the likelihood of their occurrence.Identify dependent and independent events.

Generalise conditions for dependence.Explain and justify choices related to chance.

Describes events where the second event is dependent on the first event. 4b

Writes a statement that correctly generalises the conditions for dependent events. 3Correctly justifies why the chosen prediction is correct. 5b

A

Describes independent events. 4a Lists all possible outcomes. 5c

Justifies placement of an everyday event on a chance continuum.2cJustifies why events are not dependent on each other. 3 B

Describes everyday events using the language of chance. 1Orders everyday events from least likely to most likely. 2aWrites an example of an everyday event. 2bDescribes the likelihood of an everyday event. 2cCorrectly identifies dependent and independent events. 3Lists some possible outcomes. 5c

Explains the likelihood of an everyday event using everyday language. 2c Makes a correct prediction. 5a C

Identifies an event as dependent or independent. 3, 4 Attempts to explain the likelihood of an everyday event using everyday language. 2c D

Recognises an everyday event as impossible, likely or certain. 1 E

Feedback:

Australian Curriculum

Foundation to 6 Maths - Year 4

Year 4 Achievement StandardBy the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify and explain strategies for finding unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

Content Descriptions

Number and Algebra Measurement and Geometry Statistics and Probability

Number and place value

Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

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

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Fractions and decimals

Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed

numerals. Locate and represent these fractions on a number line (ACMNA078)

Patterns and algebra

Explore and describe number patterns resulting from performing multiplication (ACMNA081)

Using units of measurement

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

Convert between units of time (ACMMG085) Use ‘am’ and ‘pm’ notation and solve simple time

problems (ACMMG086)

Chance

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

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

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

Data representation and interpretation

Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

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)

Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Content Descriptions

Number and Algebra Measurement and Geometry Statistics and Probability Solve word problems by using number sentences involving

multiplication or division where there is no remainder (ACMNA082)

Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083)

Curriculum Priorities - Pedagogy

Considerations

Prior and future curriculumRelevant prior curriculum

Students require prior experience with: recognising and representing numbers up to four digits recognising the connection between addition and subtraction recalling addition and multiplication facts for single-digit numbers solving problems using efficient strategies for multiplication describing, continuing and creating number patterns interpreting and comparing data displays conducting chance experiments and listing possible outcomes continuing number patterns involving addition and subtraction modelling and representing unit fractions using metric units for length, mass and capacity telling time to the nearest minute.

Curriculum working towards

The teaching and learning in this unit work towards the following: recalling multiplication facts to 10 x 10 and related division facts choosing appropriate strategies for calculations involving multiplication and division describing number patterns resulting from multiplication identifying unknown quantities in number sentences identifying dependent and independent events describing and evaluating different methods for data collection and representation recognising common equivalent fractions in familiar contexts locating familiar fractions on a number line

Curriculum Priorities - Pedagogy

Considerations making connections between fraction and decimal notations, up to two decimal places continuing number sequences involving multiples of single-digit numbers converting between units of time solving problems involving time duration using scaled instruments to measure temperatures, lengths, shapes and objects.

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

SustainabilityStudents will develop the knowledge, skills, values and world views necessary for people to act in ways that contribute to more sustainable patterns of living.

For further information, refer to Sustainability in the Australian Curriculum and the Learning area statements

Assessing student learning

Assessing student learningAssessment name: Investigating the nature of 10 000

Assessment description: Students use simple strategies to reason and solve number inquiry questions.

Assessment name: Recalling and using multiplication and division facts

Assessment description: Students recall multiplication and division facts, identify and explain unknown quantities and solve problems using appropriate strategies for multiplication and division.

Assessment name: Identifying and explaining chance events

Assessment description: Students identify dependent and independent events and explain the chance of everyday events occurring.In this unit, assessment of student learning aligns to the following components of the Achievement standard.By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts

and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify and explain strategies for finding unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected 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 observations, consultations and samples of student work, for example:

represent, compare and order four-digit numbers recall addition and subtraction facts apply a range of strategies to solve addition and subtraction problems of whole numbers up to four digits apply strategies to assist recall of multiplication facts represent fractions using materials and diagrams recall number facts fluently and accurately model, order and count fractions identify equivalent fractions using materials and diagrams position whole numbers and fractions on number lines labelled models of unit fractions and recording of equivalent fractions to one whole use strategies to find unknown quantities provide examples of equivalent addition and subtraction number sentences tell the time using am and pm notation use strategies to solve time problems choose appropriate personal referents read simple graduated length and temperature scales represent 10 000 in various ways automatically and accurately recall multiplication facts apply number facts and generalisations to solve extended facts complete picture and column graphs.

Monitoring task

Monitoring name: Understanding place value, fractions and operations

Monitoring description: Students demonstrate understanding of place value, operations and fractions

FeedbackFeedback in this unit may include:

recall of addition and subtraction number facts recall of 2s, 4s, 5s and 10s multiplication facts ability to read times on digital and analog clocks recall of 2s, 4s, 5s and 10s facts ability to represent 10 000 in various ways strategies used to identify unknown quantities effective data representations.

Year 4 Semester 1 Term 1 Mathematics Report Card Comment BankAssessment Task 1: Recalling and using multiplication and division facts

A B C D E

1M4A1 1M4B1 1M4C1 1M4D1 1M4E1Recalling and using multiplication and division facts

{Name} showed correct working out to find the missing values in number sentences. {She,He} correctly calculated and explained thinking to identify and verify the number of marshmallows and amount spent each day. {Name} clearly and logically explained their thinking to efficiently calculate the individual cost of a bottle of drink and the individual cost of a jar of jam.

Recalling and using multiplication and division facts

{Name} chose and accurately applies efficient multiplication and division strategies. {She,He} applied and explained a strategy relating to their number sentence or model. {Name} found the individual cost of a bottle of drink and the individual cost of a jar of jam..


{Name} recalled 2s, 4s, 5s and 10s multiplication and division facts fluently. {She,He} found a missing value in a number sentence. {Name} chose and applied a strategy to multiply and divide. {She,He} explained the problem by writing number sentences or models to find the number of marshmallows and the amount of money.


{Name} recalled some 2s, 4s, 5s and 10s multiplication and division facts. {She,He} chose and applied a strategy to multiply or divide. {Name} represented a problem by writing a number sentence or model to find the number of marshmallows or the amount of money.


{Name} recalled a 2s, 4s, 5s or 10s multiplication or division fact. {She,He} wrote a number sentence.

Assessment Task 2: Investigating the nature of 10 000

A B C D E1M4A2 1M4B2 1M4C2 1M4D2 1M4E2

Investigating the nature of 10 000

{Name} accurately transferred knowledge of numbers to complex situations. {She,He} consistently and clearly used appropriate mathematical language, materials and diagrams. {Name} developed and applied methods to gather relevant evidence for a viable answer to how much is 10 000. {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 order of number understanding to answer the inquiry question. {She,He} consistently used appropriate mathematical language, materials and diagrams. {Name} developed a method to gather evidence to support answer to how much is 10 000. {She,He} explained mathematical thinking including choices made, strategies used and conclusions reached.


{Name} recognised, represented and ordered numbers to answer the inquiry question. {She,He} applied place value to partition, rearranged and regrouped numbers to at least tens of thousands. {Name} used appropriate mathematical language, materials and diagrams. {She,He} chose a known method to gather evidence to support answer to how much is 10 000. {Name} represented and presented evidence by describing their mathematical thinking including strategies used and conclusions reached.


{Name} used aspects of mathematical language, materials or diagrams. {She,He} identified place value up to tens of thousands. {Name} followed a given method to gather evidence. {She,He} made statements about choices or strategies used when prompted.


With assistance, {Name} recognised the number 10 000. {Name} used everyday language and made isolated statements.

Assessment Task 3: Identifying and explaining chance events

A B C D E

1M4A3 1M4B3 1M4C3 1M4D3 1M4E3Identifying and explaining chance events

{Name} correctly ordered events according to their likelihood of occurrence. {She,He} wrote a statement that correctly generalises the conditions for dependent events. {Name} correctly justified why the chosen prediction is correct.

Identifying and explaining chance events

{Name} selected correct events where the second event is dependent on the first event. {She,He} explained placement of an everyday event on a chance continuum.


{Name} recognised everyday events using the language of chance. {She,He} correctly identified dependent and independent events. {Name} wrote an example of an everyday event.


{Name} identified an event as dependent or independent. {She,He} identified an everyday event known to them.


{Name} recognised an everyday event as an impossible, likely or certain event. {She,He} recognised an independent event.

Maths Pre-ModerationYear 4: 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 representations of numbers; partition and combine numbers flexibly; recall multiplication facts; formulate, model and record authentic situations involving operations; compare large numbers; generalise from number properties and results of calculations; and derive strategies for unfamiliar multiplication and division tasks.

Fractions and decimals - communicate sequences of simple fractions. Patterns and algebra - use properties of numbers to continue patterns. Using units of measurement - use appropriate language to communicate times, compare time durations and use instruments

to accurately measure lengths. Chance - compare dependent and independent events, describe probabilities of everyday events. Data representation and interpretation - collect and record data, communicate information using graphical displays and

evaluate the appropriateness of different displays.

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

Assessment Task 1: Recalling and using multiplication and division factsUnderstanding Fluency Recalls 2s, 4s, 5s and 10s multiplication and division facts fluently. Finds a missing value in a number sentence. Chooses and applies a strategy to multiply and divide..

Problem Solving and Reasoning Explains the problem by writing number sentences or models to find the number of marshmallows

and the amount of money.

Assessment Task 2: Investigating the nature of 10 000Understanding Fluency Recognises, represents and orders numbers to answer the inquiry question. Applies place value to partition, rearrange and regroup numbers to at least tens of

thousands. Uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Chooses a known method to gather evidence to support answer to how much is 10 000. Represents and presents evidence.

Describes mathematical thinking including strategies used and conclusions reached.

Assessment Task 3: Identifying and explaining chance eventsUnderstanding Fluency

Recognises everyday events using the language of chance. Correctly identifies dependent and independent events.

Problem Solving and Reasoning Writes an example of an everyday event.

Scan and Assess

Prioritise

Develop and Plan

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: recall of addition and subtraction number facts recall of 2s, 4s, 5s and 10s multiplication facts ability to read times on digital and analog clocks recall of 2s, 4s, 5s and 10s facts ability to represent 10 000 in various ways strategies used to identify unknown quantities effective data representations.

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: Recalling and using multiplication and division factsUnderstanding Fluency Recalls 2s, 4s, 5s and 10s multiplication and division facts fluently. Finds a missing value in a number sentence. Chooses and applies a strategy to multiply and divide..

Problem Solving and Reasoning Explains the problem by writing number sentences or models to find the number of marshmallows and the amount of money.

Assessment Task 2: Investigating the nature of 10 000Understanding Fluency Recognises, represents and orders numbers to answer the inquiry question. Applies place value to partition, rearrange and regroup numbers to at least tens of thousands. Uses appropriate mathematical language, materials and diagrams.

Problem Solving and Reasoning Chooses a known method to gather evidence to support answer to how much is 10 000. Represents and presents evidence.

Describes mathematical thinking including strategies used and conclusions reached.

Assessment Task 3: Identifying and explaining chance eventsUnderstanding Fluency

Recognises everyday events using the language of chance. Correctly identifies dependent and independent events.

Problem Solving and Reasoning Writes an example of an everyday event.

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

Assessment Task 1: Recalling and using multiplication and division factsUnderstanding Fluency Chooses and accurately applies efficient multiplication and division strategies.

Problem Solving and Reasoning Applies and explains a strategy relating to their number sentence or model. Finds the individual cost of a bottle of drink and the individual cost of a jar of jam..

Assessment Task 2: Investigating the nature of 10 000Understanding Fluency Recalls and uses appropriate order of number understanding to answer the inquiry question. Consistently uses appropriate mathematical language, materials and diagrams

Problem Solving and Reasoning Develops a method to gather evidence to support answer to how much is 10 000. Explains mathematical thinking including choices made, strategies used and conclusions reached.

Assessment Task 3: Identifying and explaining chance eventsUnderstanding Fluency Selects correct events where the second event is dependent on the first event

Problem Solving and Reasoning Explains placement of an everyday event on a chance continuum.

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

Assessment Task 1: Recalling and using multiplication and division factsUnderstanding Fluency Shows correct working out to find the missing values in number sentences.

Problem Solving and Reasoning Correctly calculates and explains thinking to identify and verify the number of marshmallows and amount spent each

day. Clearly and logically explains thinking to efficiently calculate the individual cost of a bottle of drink and the individual

cost of a jar of jam.

Assessment Task 2: Investigating the nature of 10 000Understanding Fluency Accurately transfers knowledge of numbers to complex situations. 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 answer to how much is 10 000. Represents and presents evidence logically. Clearly explains mathematical thinking including choices made, strategies used and conclusions reached.

Assessment Task 3: Identifying and explaining chance eventsUnderstanding Fluency Correctly orders events according to their likelihood of occurrence.

Problem Solving and Reasoning Writes a statement that correctly generalises the conditions for dependent events. Correctly justifies why the chosen prediction is correct.

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 FeedbackLesson 1Comparing and ordering four-digit numbers Example learning sequence

Establish learning context Compare four-digit numbers Order four-digit numbers

Evidence of learningCan the student:

Identify numbers greater or less than a given number?

Order numbers on a number line? Locate numbers on a number line?

Lesson 2Partitioning four-digit numbers Example learning sequence

Establish learning context Partition four-digit numbers into standard place-

value parts Partition four-digit numbers into non-standard place-

value parts


Represent standard four-digit place-value partitioning with materials?

Record standard and non-standard place-value partitions as number sentences?

Represent non-standard four-digit place-value partitioning with materials and record as number sentences?

Lesson 3Applying place-value understanding to four-digit numbers Example learning sequence

Establish learning context Demonstrate place-value understandings


Identify numbers up to four digits in everyday contexts?

Classify numbers using the symbols < and >? Order sets of four-digit numbers? Recognise that the place-value pattern is built on

multiplication and division operations?

Lesson 4Practising recalling addition and subtraction facts Example learning sequence

Establish learning context Recall addition number facts Recall related subtraction number facts Add and subtract with multiples of 10 Use addition number facts


Recall addition and subtraction facts? Identify the relationships between addition and

subtraction facts? Apply knowledge of number facts to extended

calculations?

Lesson 5Practising efficient computation strategies Example learning sequence

Establish learning context Solve addition problems using mental computation Solve subtraction problems using mental

computation Solve addition and subtraction problems in context


Use a range of strategies for mental computation? Solve addition and subtraction problems in context?

Lesson 6Investigating patterns involving multiples Example learning sequence

Establish learning context Investigate multiples of 2, 4, 5 and 10 Practise 2, 4, 5 and 10 multiplication facts


Identify multiples of whole numbers, including common multiples?

Recognise and use patterns and relationships?

Teaching Sequence FeedbackLesson 7Extending multiplication facts Example learning sequence

Establish learning context Explore commutativity Use patterns to extend number facts


Identify related multiplication facts? Apply number-fact knowledge to solve extended

multiplication facts? Recognise and use patterns and relationships?

Lesson 8-11Investigating the nature of 10 000Example learning sequence

Establish learning context Explore number representation (Discover) Plan how to explore the question (Devise) Follow plans to collect and review evidence

(Develop) Explain results and draw conclusions (Defend) Explore further learning opportunities (Diverge)


Identify authentic contexts of the application of 10 000?

Identify value and relative size of 10 000? Justify the representation? Example learning

sequence

Lesson 12-13Identifying multiplication and division patterns (2s, 4s, 5s, 10s)Example learning sequence

Establish learning context Investigate patterns involving multiples of 2, 4, 5

and 10 Identify multiplication patterns Solve multiplication and division word problems


Apply 2s, 4s, 5s and 10s facts to complete extended facts and patterns of multiples of 2, 4, 5 and 10?

Describe and continue patterns of multiples of 2, 4, 5 and 10?

Describe and continue number patterns resulting from multiplication?

Solve multiplication and division word problems?

Lesson 14Exploring equivalence Example learning sequence

Establish learning context Identify equivalence and non-equivalence Explore relationships between quantities


Explain their understanding of equivalence? Use the comparative symbols (=, ≠, < and >) to

describe the relationship between numbers in equations and inequations?


Lesson 15Identifying unknown quantities Example learning sequence

Establish learning context Represent addition and subtraction situations Explore relationships between addition and

subtraction

Evidence of learningCan the student: Describe addition and subtraction facts using

numbers and symbols? Show addition and subtraction facts using

materials? Identify unknown quantities in number sentences?

Lesson 16Finding unknown values Example learning sequence

Establish learning context Establish equivalence to identify unknowns

Determine relationships between unknown values


Apply a range of strategies to calculate unknown quantities?

Lesson 17Assessing student learning Example learning sequence

Understand the assessment Review the Guide to making judgments and

understand the standards A–E Conduct the assessment

Assessment purposeTo recall multiplication and division facts, identify and explain unknown quantities and solve problems using appropriate strategies for multiplication and division.

Teaching Sequence Feedback

Lesson 23Investigating fractions Example learning sequence

Establish learning context Investigate fractions in the halving family by

partitioning models Identify the meaning of the fraction symbol Investigate equivalent fractions for one whole


Model and represent halves, quarters and eighths using a range of materials, diagrams and symbols?

Identify fractions equivalent to one whole?

Lesson 24

Investigating equivalent fractions and fraction models Example learning sequence

Establish learning context Identify equivalent fractions for whole numbers Investigate halving of other fraction models


Identify the improper fractions equivalent to whole numbers?

Represent halves, quarters and eighths using a variety of fraction models?


Lesson 25

Representing and counting fractions Example learning sequence

Establish learning context Investigate relative number Represent mixed numerals on number lines Count by halves, quarters and eighths


Apply partitioning to represent fractions on number lines?

Count by halves, quarters and eighths along number lines?

Use number lines to solve simple addition fraction problems?

Recognise and use patterns and relationships between fractions and whole numbers?

Lesson 26

Applying fractional understanding to solve problems Example learning sequence

Establish learning context Sort, compare and order fractions around

benchmark numbers Practise calculating equivalent fractions in

context


Compare and order fractions in relation to benchmark numbers?

Use modelling or diagrams to solve fractions problems?

Lesson 27

Understanding place value, fractions and operations Example learning sequence

Establish learning context Apply place-value understanding (Monitoring task) Apply understanding of operations Apply understanding of fractions


Work fluently and accurately, identifying, representing and calculating with whole numbers up to four digits, and fractional numbers (halves, quarters, eighths), including mixed numbers and improper fractions?

Recognise and use patterns and relationships between fractions and whole numbers?

Lesson 18

Investigating units of time Example learning sequence

Establish learning context Explore the standard units for measuring time Investigate the relationship between units of time Tell the time to the quarter hour


Convert between seconds, minutes and hours? Read and show times to the quarter hour on digital

and analogue clocks?


Lesson 19

Telling the time using ‘am’ and ‘pm’ notation Example learning sequence

Establish learning context Tell the time to the minute Introduce am and pm in relation to 12-hour

time


Read and show times to five-minute intervals on digital and analog clocks?

Read and show minutes to and past the hour on digital and analog clocks?

Identify events and activities that occur in ‘am’ and ‘pm’ times?

Lesson 20

Calculating duration of time Example learning sequence

Establish learning context Solve simple time problems Convert between units of time to solve

problems


Solve time problems using an analog clock face? Calculate the duration of time using a number line? Convert between units of time to solve problems?

Lesson 21

Measuring length using informal units Example learning sequence

Establish learning context Create informal unit to measure length Establish formal units


Identify relationships between informal units of length to

measure? Read and identify formal units of measurement?

Lesson 22

Measuring length using formal units Example learning sequence

Establish learning context Introduce measuring length using graduated scale Measure length using scaled instruments


Measure and compare lengths using formal units? Measure a variety of lengths (width, height, girth)

using the graduated scales on different tools (tape measure, ruler)?

Lesson 28

Comparing and ordering everyday events)Example learning sequence

Establish learning context Identify and compare everyday events Order events on continua according to their

likelihood of occurring


Describe the occurrence of everyday events using chance terms?

Order chance terms on a continuum? Order everyday events on a continuum?

Lesson 29

Identifying dependent and independent events Example learning sequence

Establish learning context Identify dependent and independent events Conduct chance experiments


Identify the difference between a dependent and an independent event?

Describe an event as dependent or independent and use real-world examples to support decisions?

Explain why certain events cannot occur at the same time?

Lesson 30

Assessing student learning Example learning sequence

Understand the assessment Review the Guide to making judgments and

understand the standards A–EConduct the assessment

Assessment purposeTo identify dependent and independent events and explain the chance of everyday events occurring..


Lesson 31

Collecting data through observations and surveys Example learning sequence

Establish learning context Compare data collection methods and sources Collect data by conducting an observation Collect data by conducting a survey


Identify data collection methods and sources? Compare data collection methods and sources? Collect data through observation? Make judgments about questions suitable for use in

a survey? Conduct a survey and collate data in a table??

Lesson 32

Presenting collected data in picture graphs and column graphs Example learning sequence

Establish learning context Investigate picture graphs as data representations Construct picture graphs using collected

observation data Investigate column graphs as data representations Construct column graphs using collected

survey data


Interpret picture graphs showing one-to-one and/or one-to-many correspondence?

Create a picture graph from collected data? Identify the purpose and intent of column graphs? Create a column graph from collected data?

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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