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NA4-2: Understand addition and subtraction of fractions, decimals, and integers.

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Elaboration on this Achievement Objective

This means students will understand decimals as fractions, and be able to express decimals in fraction form and vice versa, for example 2.47 = 2 + 4 tenths + 7 hundredths (2 + 4/10 + 7/100 ), or 247 hundredths (247/100). They should solve addition and subtraction problems with decimals and with fractions (denominators must be related multiples), for example 13.2 – 5.79 = 7.41 and 3/4 + 7/8 = 13/8 = 1 5/8 by choosing appropriately from mental, machine and paper methods. Students should apply the strategies used for mental calculation with whole numbers to addition and subtraction of decimals, including standard place value, compensation after rounding, and applying inverse (reversing). Formal written algorithms for decimal addition and subtraction should be taught at Level Four after students have the place value knowledge required to understand them.

 

Teaching resources for this Achievement Objective
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Disappearing Dollars

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. A PDF of the student activity is included.

add and subtract integers using money context

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Dollars and Bills

Level Four
Number and Algebra
Numeracy activities

Solve addition and subtraction problems with integers (positive and negative numbers).

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Dropping and rising temperatures

Level Four
Number and Algebra
Numeracy activities
Understand integers.
Solve addition and subtraction problems with integers.
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Easy fraction game

Level Four
Number and Algebra
Numeracy activities
To give students practise in adding fractions that match the descriptions eg. 1/8 + 1/4 ‘add to less than 1’. This can be used as a class starter or as an independent game.

add fractions with related denominators.

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Egyptian Fractions

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

add related fractions

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Expanding with Decimals

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

show understanding of decimal place value

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Flying Home

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

add and subtract decimals

use rounding to estimate a multiplication problem

finda percentage of a decimal number

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Fractional Magic Squares

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Perform addition with fractions.
  • Know the idea of, and be able to construct, magic squares.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Gentle Giants

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

order decimals to 3 decimal places

add and subtract decimals

 

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Getting partial to decimals

Level Four
Number and Algebra
Units of Work
This unit supports students to understand the place value structure of decimals and to carry out addition and subtraction with decimal numbers to three places.
  • Understand that decimals are a kind of fraction.
  • Add and subtract decimals to three decimal places.
  • Find decimal values for fractions through practical modelling.
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Getting partial to fractions

Level Four
Number and Algebra
Units of Work
In this unit students partition a length model into equal parts, to create unit fractions. Students form non-unit fractions (e.g. 3/4 and 7/8) and develop strategies to find different names for the same fraction (equivalent fractions). Fractions are added and compared to find the difference and a...
  • Find equivalent fractions.
  • Compare the size of fractions to order them.
  • Find the difference between two fractions by subtraction.
  • Add fractions.
  • Find a fraction of a whole number amount.
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Going bananas

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving problems using integer values.
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Going for Gold!

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

order decimals to 3 decimal places

add and subtract decimal numbers

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Go Negative

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Perform calculations with negative fractions.
  • Devise and use problem solving strategies mathematically (e.g. be systematic, draw a picture).
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Having fun with the vertical algorithm

Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice and develop their number properties. Some are suitable for homework, others require follow-up during teaching sessions
solve addition and subtraction problems with 4 digit numbers in a written algorithm
solve addition and subtraction problems involving decimals in a written algorithm
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Hills and Dales

Level Four
Number and Algebra
Numeracy activities

Solve addition and subtraction problems with integers (positive and negative numbers).

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How can Two Decimals so Ugly make one so Beautiful

Level Four
Number and Algebra
Numeracy activities

Solve problems that involve adding and subtracting decimals.

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How many pieces? (years 4-6)

Level Two
Level Three
Level Four
Integrated
This counting collections activity engages students in finding the number of sheets in a roll of toilet paper.
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How many pieces? (years 7-10)

Level Four
Level Five
Integrated
This counting collections activity engages students in identifying which roll of toilet paper is better value.
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Integer Links

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

add and subtract integers

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Integers

Level Four
Number and Algebra
Units of Work
This unit helps students to develop procedural fluency with integers and have conceptual understanding of integers in the real world.
  • Understand everyday application of integers.
  • Add and subtract positive and negative integers.
  • Use models to explain why subtraction of a negative integer has a positive effect.
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Integer Slam

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

add and subtract integers

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Integer Zap

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. A PDF of the student activity is included.

add and subtract integers

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Investigating Integers

Level Four
Number and Algebra
Units of Work
This unit begins with Freudenthal’s (1983) annihilation model for demonstrating the addition and subtraction of integers then goes on to introduce other representations. It is designed for students who are able to choose appropriately from a broad range of mental strategies to estimate answers and...
  • Solve simple addition and subtraction equations involving integers.
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It pays to save

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a problem involving decimals (currency) and percentages.