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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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Investment Choices

Level Three
Level Four
Integrated
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. It is also a level 3 statistics activity.A PDF of the student activity is included.

find a percentage of a whole number (calculate interest rates)

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Invisible Resources

Level Four
Integrated
Figure It Out activities
This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.A PDF of the student activity is included.

Students will:

  • perform calculations with percentages involving time and volume.

Students should discover that:

  • one ratio (for example, burn times) may be used to discover another (for example, relative amounts of gases in air).
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Involving Interest

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 percentage of whole numbers

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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.
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It takes a village

Level Four
Integrated
Units of Work
In this unit students develop understanding of the financial challenges faced by superannuitants in their local community. As part of this, they research the community resources and services that are available to support the older citizens and implement a (short term) programme of help for at least...
  • Apply number knowledge and strategies to bank statements and budget problems.
  • Consider and apply protocols around the manageability of data collection and data safety.
  • Use research information to inform an investigation.
  • Determine appropriate variables and data collection methods.
  • Design a survey format300
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Jellybean equal shares

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in equally partitioning a set of objects among four parties.
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Juggling A Business

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.

use multiplicative strategies to solve money problems

use addition and subtraction to solve money problems

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Keep Your Shirt On

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

identify which graph best represents the data

use multiplicative strategies to calculate costs

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Making Flubber

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using fractions, proportions and percentages to solve a problem.
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Making Money

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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Market Day

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 10% and 20% of money amounts

use addition and subtraction to solve money problems

 

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More complex discounts

Level Four
Number and Algebra
The purpose of this activity is to support students in calculating prices after any percentage discount is applied.
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More complex fractions as percentages

Level Four
Number and Algebra
The purpose of this activity is to support students in developing their knowledge of fraction to percentage conversions. The problems are extended to include wholes that can be reduced to simple fractions using common factors.
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More complex percentage increases

Level Four
Number and Algebra
The purpose of this activity is to support students in calculating the new price after a percentage increase occurs.
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Movie parts

Level Four
Number and Algebra
The purpose of this unit is to engage students in applying their knowledge and understanding of fractions, decimals, and percentages when identifying and generalising a linear trend. Students develop these skills, related to Multiplicative Thinking and Patterns and Relationships (e.g. understanding...

  • Apply knowledge of rates and ratios, and reasoning with linear proportions, to solve problems involving time.

  • Find and describe a rate of change for given data from a linear trend. 

  • Find and describe a linear trend.

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New Car Capers

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 percentages of a whole number

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New Zealand Made?

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.

use rates to calculate exhange rates

find a percentage of a number

use multiplicative strategies to solve money problems

 

 

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On the Campaign Trail

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.

fidn a fraction of a whole number

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On Top of the World

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.

explore relative values

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On Your Bike, Mike

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

analyse survey questions

interpret information from graphs

find percentages of numbers

use addition and subtraction to solve money problems

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Part-time Work

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.

use mental strategies to solve multiplication problems involving money

find a percentage of a money amount

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Paying the Bills

Level Three
Level Four
Number and Algebra
Figure It Out activities
This is a level 3 and 4 number 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.

find 1/3 of a money amount

use addition and subtraction to solve money problems

use multiplication to solve money problems

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People Power

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.

round numbers

estimate a percentage

match a percentage to a shaded region of a whole

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Percentage increases

Level Four
Number and Algebra
The purpose of this activity is to support students in calculating the new price after a percentage increase occurs.
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Percentage Passes

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.

convert fractions to percentages

find mean of a set of numbers