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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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6 Minus 8 Does Work!

Level Four
Number and Algebra
Numeracy activities

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

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Adding and subtracting decimals

Level Four
Number and Algebra
The purpose of this activity is to support students in solving problems that require the addition and subtraction of decimals.
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Adding in Parts

Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are designed for students to use independently to practise number properties.
  • Solve addition problems with whole numbers by adding in parts.
  • Solve addition problems with decimnal numbers by adding in parts.
  • Use equal addition strategies to insert numbers to balance addition equations.
  • Use equal addition strategies to insert numbers and letter symbols to balance algebraic300
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Adding integers

Level Four
Number and Algebra
The purpose of this activity is to support students in understanding how addition applies to positive and negative integers. Students often develop an over-generalisation that “addition makes bigger”, that is the sum (answer) is always larger than the beginning addend. With the addition of a...
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Adding with Decimal Fractions

Level Four
Number and Algebra
Numeracy activities

Solve problems that involve adding and subtracting decimals.

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Addition/Subtraction Strategies

Level Three
Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice number properties and strategies for addition and subtraction.
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A fair dip

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a financial problem using decimal arithmetic techniques.
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A Measured Response

Level Four
Integrated
Units of Work
The purpose of this unit is to have students identify a need, plan a response, seek feedback, design and build a ‘product’, applying number, measurement and technology knowledge and skills.
  • Identify a utility need or opportunity within the school and plan a response .
  • Create a design incorporating key attributes identified.
  • Investigate quality and comparative costs of possible construction materials.
  • Cost ‘fit for purpose’ construction materials and prepare a budget.
  • Draw plans300
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A Model World

Level Four
Integrated
Units of Work
The purpose of this unit is for students to apply and refine their measurement skills and to develop an understanding of enlargement and reduction, through making scale models to be used in a short, animated stop-motion film.
  • Understand and describe proportion using the language of mathematics.
  • Understand the principles of scale.
  • Create scale drawings.
  • Calculate scale dimensions.
  • Make accurate metric length measurements.
  • Understand that the value of the scale factor of a reduction is less than 1 and for an enlargement is300
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Beefing Up Business

Level Four
Integrated
Figure It Out activities
This is a level 4 number, algebra and statistics activity from the Figure It Out series. A PDF of the student activity is included.

use addition to sovle money problems

use multiplication and division to solve problems

find percentage of a number

solve problems involving ratios

find fraction of a number

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Branching Out

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.

multiply decimals with multiples of ten

operate on fractions and decimals

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Bucket balance

Level Four
Number and Algebra
Numeracy activities
Understand integers.
Solve addition and subtraction problems with integers.
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Buying Batteries

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.

find fractions of money amounts

add money amounts

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Charu in a Pickle

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

find a percentage of a decimal number

solve addition and subtraction problems

compare prices by using proportions

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Chilly Heights

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.

solve addition and subtraction problems involving integers

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Comparing apples with apples 2

Level Four
Level Five
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practice number properties.

Addition and subtraction of fractions with unlike denominators

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Comparing Chalk and Cheese

Level Four
Number and Algebra
Numeracy activities

convert unlike units in order to add and subtract them

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Compatible decimal fractions

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.

Use compatible numbers to solve addition problems with decimal fractions (tenths) (Exercises 1-5)
Use compatible numbers to solve subtraction problems with decimal fractions (tenths) (Exercise 6)

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Create A Question

Level Four
Number and Algebra
Problem solving activities
  • Use their mathematical knowledge to invent problems.
  • Solve other students' problems.
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Cuisenaire Rod Fractions: Level 4

Level Four
Number and Algebra
Units of Work
This unit introduces the fact that fractions come from equi-partitioning of one whole. Therefore, the size of a given length can only be determined with reference to the size of one whole. Usually the one must be defined in context.
  • Name the fraction for a given Cuisenaire rod with reference to one (whole).
  • Give the relationship between one Cuisenaire Rod and another, especially when one rod is a fraction of the other.
  • Add and subtract fractions by expressing fractions as equivalents with the same denominator.
  • Order fractions300
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Cycling On...

Level Four
Number and Algebra
Figure It Out activities
This is a level 4 number and level 4 measurement 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.

find fractions of time

calculate average speed

interpret timetable

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Dallying with Decimals

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 available.

add and subtract decimals

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Dash and Splash!

Level Four
Level Five
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 decimal numbers

order decimals to 2 decimal places

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Decimal Fraction Buddies

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.

find decimal addition pairs

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Decimal Fractions – Tenths

Level Four
Number and Algebra
Secondary activities
These exercises and activities are for students to use independently of the teacher to practise number properties.

Solve addition and subtraction problems involving decimal tenths.