Numeracy Unit of Work Edited

Achievement Targets (AC):

Year 5 (Working towards this achievement standard throughout Year 5)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 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 compare and 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 find unknown quantities in number sentences. 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.

Year 6 (Working towards this achievement standard throughout Year 6)By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian place. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages.

Year 7 (Working towards this achievement standard throughout Year 7)By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notations and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties of numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two parallel lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane.

Unit of Work: Mathematics Year Level: 5/6/7

Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stem-and-leaf plots and dot-plots.

Unit Outline (Weekly, these are not lesson plans, BUT what you plan to cover throughout the week taken from your Unit Overview ):

KEY: Whole Class ∆ Small Group Ω Individual

Week(when)

Selected Learning Outcomes(CF or AC)

Teaching and Learning Activities(what and how)

Group Structure(classroom arrangement)

Resources(teaching aids, student requirements)

Assessment TypeF –FormativeS-SummativeD-Diagnostic

6 ACMNA291, ACMNA123

Mental mathematics:- JEMM – Junior

Elementary Math Mastery. Brief, mental quizzes, featuring repetitive questions with visual prompts. Gradually increasing in difficulty, serving to map student progress and encourage fluency skills with mental processes. 2x lessons per day.

JEMM book and slides Formative assessment

ACMNA130 Multiplying and dividing by powers of 10:

- Graph paper, using a ∆ ‘Decimal Fractions’ – First Steps in Mathematics – Number (Book 1), p.73

modified version of ‘Decimal Fractions’

- Begin with integers – effects of multiplying by 10, 100, 1,000

- Introduce decimals, moving the decimal place

- Use place value charts to indicate

- Link back to integers

http://www.amsi.org.au/ESA_middle_years/Year6/Year6_md/Year6_1c.html#teaprop-4

https://schoolsequella.det.nsw.edu.au/file/611cbf36-d463-4a6d-b969-6353ad070bf8/1/mult_10_100.zip/mult_10_100/index.html

ACMNA105 Integers and decimals on a number line:

- Begin with number line from 0-1 in tenths. Laminated number cards, students to work in partners to decide where they go and put them up on a class number line.

- Students to work in small groups to measure their height and record it in metres (i.e. as a decimal), then order themselves from shortest to tallest, and place their height card where they belong. Make comparisons between decimal measurements, using the order as a guide.

- Verify answer/order they got based on the

∆

Ω

Decimal place value chart (Self made)

Height card for each student (self-made)Height chart for each student (self made)

Tape measures!Tape measures

Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), p.108

Formative assessment – number line





numbers on the card with visual check. Right/wrong, where could they have gone wrong (in the measuring, in the recording, in the comparing?)

- Assign groups for students – give them a number and get them into groups with the same number?

- Explicitly show the students how to measure and record. Move around to check that each student is measuring and recording accurately.

Assist in measuring, formative assessment – check for ability to use measurement, estimating to check validity of answer, etc

-- Use place value chart to

order decimals, and to reason why a number is larger or smaller than another.

- LAMINATED P.V. chart – students to write and reuse. Model how to write on it.

- Check for

understanding that more digits in a number does not mean a larger number

- Use whiteboards to get students to select which is larger out of the two numbers shown

-

7-8 ACMNA291, ACMNA123



JEMM book and slides write important details on board Formative assessment

Record student achievement – informal, over the shoulder marking, student self-marking

ACMNA105 Integers and decimals on a number line:

- Use place value chart to order decimals, and to reason why a number is larger or smaller than another. Revision of previous activity

- Check for understanding that more digits in a number does not mean a larger number

∆

Ω

Decimal place value chart


‘Peg Up’ activity – First Steps in Mathematics – Number (Book 1), p.71

Summative assessment - Sequencing times or distances activity

- Which is bigger? – Children begin in the middle of the room, and two decimals are shown on either side of the board. Children run to the side corresponding with the larger number. Children to reason why that number is bigger.

- Problem solving task – finding the costs of items from a variety of clues. Set up activity as a shop, assigning post-it notes with prices on them to the correct objects in accordance with the clues given.

- ‘Peg Up’ activity

- Sequencing times or distances – use data from Olympic finals, have students order and arrange results from winner down to last place. High ability students – calculate time/distance between each athlete and the winner or world record.



Elementary Math Mastery. Brief, mental

JEMM book and slides

60 multiplication questions, answers and timer

Formative assessment

quizzes, featuring repetitive questions with visual prompts. Gradually increasing in difficulty, serving to map student progress and encourage fluency skills with mental processes. 2x lessons per day.

- 60 multiplication – a display of 60 multiplication problems are displayed on the board and students have a time limit in which to complete as many as possible.

ACMNA131

Introduction to fractions:- First Steps in

Mathematics – Number (Book 1), p., ‘Diagnostic Task’.

- Block of chocolate to model fraction division – dividing into halves, quarters, etc. Emphasising equivalent fractions throughout.

- Packets of smarties to emphasis fractions as ‘parts of a group’, not just ‘pieces of a pie’

- Class activity – making play dough for subsequent activity

-

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Ω

First Steps in Mathematics – Number (Book 1), pp.94-100, and pp.106-112, depending on ability.

Block of chocolate

Play dough, fraction tub

‘Paper folding’ – Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), p.59

‘Fraction Circles’, First Steps in Mathematics –Number (Book 1), p.129, ‘Equivalent Fractions’, p.130

Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), pp.59, 65-68

Diagnostic assessment – First Steps in Mathematics diagnostic task

Formative Assessment – measureme

- Play dough and fraction tub to scaffold understanding of fractions of a whole.

- Incorporate both uses of fractions – in terms of ‘parts of a pizza’ and ‘objects in a box’.

- ‘Paper folding’ – paper strips, introduce to equivalence

- Equivalence activities with fractions

- ‘Equivalent fractions matching card game’ – introduce, play as memory or snap. Reasoning throughout the activity – what have you turned over, what might you be looking for? Are those two cards equivalent? Which is bigger? Which is smaller?

- Incorporate mix numerals and improper fractions

- Include basic simplification of fractions while looking at equivalence, e.g. 3/6=1/2, 2/4=1/2.

nt, following a procedure

ACMNA131

Equivalent fractions and decimals:

- Begin using fractions /10, /100. Use graph paper to make connections between fractions and decimals, or an appropriate grid.

- Draw common fractions (e.g. 1/2, 1/4, 1/5) on 100s grid and then convert to decimals.

-

‘100-grid and recording sheet’, Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), p.138, or graph paper

ACMMG140

3D Shapes:- Constructing prisms and

pyramids

- Estimating the net of a prism and/or pyramid – drawing and attempting to make it form the desired shape.

- Folding paper cut outs of nets to create prisms and pyramids

- Drawing and identifying nets of prisms and pyramids.

-

Ω

Paper

Nets of 3D shapes



Elementary Math Mastery. Brief, mental quizzes, featuring repetitive questions with visual prompts. Gradually increasing in difficulty, serving to




map student progress and encourage fluency skills with mental processes. 2x lessons per day.


Equivalent fractions and decimals:

- Explicit teaching – division of the numerator by the denominator to get the equivalent decimal. Verify through common fractions (e.g. 1/2, 1/4).

- ‘Concentration’ activity to help develop fluency.

- ‘Fraction/Decimal/Percentage cards’

- Bingo – ask questions in fractions and have students list answers in decimals, or switch.

-

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Ω

‘Concentration’ – First Steps in Mathematics – Number (Book 1), p.148

‘Fraction/Decimal/Percentage cards’ – Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), pp.137, 139-142. Exclude percentage cards, and focus solely on fraction and decimal cards

Bingo boards

Formative, informal assessment – bingo

ACMNA102, ACMNA125

Compare and order fractions, place related fractions on a number line:

- Begin with unit fractions (1/2, 1/3, 1/4, 1/5…),

∆ Diagrams of unit fractions

Number line

Summative assessment – number

with pictorial support. Place fractions on a number line, noting how the portions get smaller as the denominator gets larger.

- ‘Ropes’

- Extend to include other basic fractions. Order on number line with pictorial support.

-

‘Ropes’ – First Steps in Mathematics – Number (Book 1), p.136

‘Equivalent fraction domino’ cards - Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), pp.75-77

line

ACMMG108 Units of measurement:- Focusing on common

units of measurement

- Length o kmo mo cmo mm

- Area o km2

o m2

o cm2

o mm2

- Masso to kgo g

- Capacityo Lo mL

Ω

Ways of measuring various items

Objects that can be used to estimate different measurements


- Volumeo cm3

o m3

- Timeo Hourso Minuteso Seconds

- How different things are measured, what units are appropriate to use and when

- Estimating what measurements to use

-





-




ACMNA103 Add and subtract fractions with the same denominator:

- Begin with graph paper or other images, drawing out representations of the fractions and adding or subtracting, with written documentation underneath.

- Model, draw and then move to simply writing.

- Fraction spinners to help develop fluency

- Worksheet to check understanding and capability

-

Ω

Graph paper

Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), pp.87, 91-92. Alter spinners so that all numbers have the same denominator, the make it easier to work with


Formative assessment – worksheet.

ACMNA126 Add and subtract fractions with similar or related denominators:

- Revise equivalent fractions

- Practice converting between related decimals (multiplying or dividing by a common factor). Draw images to show equivalence.

- Worksheet to check understanding and capability

∆


Australian Curriculum Mathematics Resource Book: Number and Algebra (Year 6), p.94.

Summative assessment – worksheet.

ACMMG108 Converting between units of measurement:

- Converting between units of length, volume and capacity

- Decimal representations

Numeracy Unit of Work Edited

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