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NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.

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Elaboration on this Achievement Objective

This means students will understand that finding a decimal or percentage of an amount involves finding a fraction of that amount, for example 40% of 56 = 0.4 x 56 = 4 x 5.6 = 22.4. They should be able to solve problems of the form a/b x c = d (a,b,c and d are whole numbers), where any one of the numbers is not known, for example 4/7 x box. = 24 (Four-sevenths of what number is twenty-four?) or box.% of 76 = 19 (What percentage of seventy-six is nineteen?). Students should be able to multiply fractions with understanding, for example 2/3 x 3/5 = box. as two-thirds of four-fifths, and use their multiplicative understanding of place value to solve multiplication and division problems with simple decimals, for example 1.6 x 0.4 = box. as 16 x 4 ÷ 100 = 0.64 and 24 ÷ 0.3 = box. as 24 ÷ 3 x 10 = 80.

 

Teaching resources for this Achievement Objective
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Accident-prone

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 fractions of whole numbers

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All Bottled Up

Level Four
Number and Algebra
Figure It Out activities
This is a level 3 number link activity from the Figure It Out series. It relates to Stage 6 of the Number Framework. A PDF of the student activity is included.

find a fraction of a whole number

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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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Bargain Bonanza

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.

find fractions of a whole number

find a percentage of a whole number

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Bargain Busters

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 percentages

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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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Big Numbers

Level Four
Number and Algebra
Picture book activities
This is an activity based on the picture book Big Numbers
  • Students will be able to create a model of the “whole” of a specific length of time and use a meaningful scale to illustrate fractions within that length of time.
  • Students will be able to demonstrate an understanding of the mathematical relationships between of units of time.
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Bits and Pieces

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.

find fractions of a number

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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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Carrie's first cubes

Level Four
Integrated
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the properties of 3-D shapes to solve a problem.
  • Visualise 3-D objects.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
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Census Sense

Level Three
Level Four
Number and Algebra
Figure It Out activities
This is a level 3 and 4 number link activity from the Figure It Out series. It relates to Stage 6 and 7 of the Number Framework. A PDF of the student activity is included.

order whole numbers

find a percentage of a whole number

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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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Chocolate Chip Feast

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 fractions

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Choices

Level Four
Number and Algebra
Units of Work
This unit is about making best option decisions in real-life situations based on cost. Common examples of such decisions are explored, including the cost of taxis, cooking times, hire cars, and mobile phones.
  • Calculate the cost of hiring a taxi, hiring a car, and using a phone, and the cooking time for meat.
  • Compare the costs of different plans.
  • Represent linear relationships using graphs.
  • Use graphs to make decisions about the best deal.
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Choosing Classes

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in working with common fractions, decimals and percentages interchangeably, to solve a problem.
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Clothes Spree

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 percentages of  whole numbers

find fractions of whole numbers

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Colour-coding

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

Level Four
Number and Algebra
The purpose of this activity is to support students in using percentages to compare two amounts in both directions, smaller to larger and larger to smaller.
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Comparing ratios

Level Four
Number and Algebra
The purpose of this activity is to support students in comparing ratios that do not have a common part or whole. They do so by using their knowledge of fractions, and by expressing the part-whole relationships as fractions.
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Comparing ratios with a common part

Level Four
Number and Algebra
The purpose of this activity is to support students in comparing ratios with a common part but different whole. They do so by creating and comparing fractions.
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Compound Interest

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.

calculate the interest rate on money deposits

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Conversion Cousins - Part 2

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.

find fractions, decimals, percentages of a whole number

know equivalent fractions, decimals and percentages

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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