NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Elaboration on this Achievement Objective
This means students will understand calculations involving fractions, decimals, percentages and integers. It assumes accuracy in calculation and the exercising of appropriate choice between mental, written and machine methods given the complexity of the numbers involved and the significance of the calculation in the context of the problem. Understanding also implies the prudent use of estimation to check the reasonableness of calculations and as an end in itself where approximations are sufficient.
Students should be able to explain the calculation steps (procedures) they followed and justify those steps by describing the quantities involved. For example, the calculation 1.4 x 0.6 = 0.84 might be justified as 14/10 x 6/10 = 84/100 or 14 x 6 = 84 and the size of answer being about half of 1.4.
The problems solved should involve result unknown, for example 56% of 38 = .gif){kind=small}
, change unknown, for example .gif){kind=small}
% of 38 = 21.28, or start unknown, for example 56% of .gif){kind=small}
= 21.28.
Teaching resources for this Achievement Objective
Estimate and find percentages of whole number and decimal amounts.
Numeracy activities
Number and Algebra
Level Five
This is a level 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.
find mean, median, mode of data construct a graph interpret data on a graph comapre different graphs and decide which shows the data most clearly
Figure It Out activities
Statistics
Level Five
Use the numbers facts with digits to solve a problem; Use a systematic approach to get the number of ways that four numbers can add to 9.
Problem solving activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
find percentages of whole numbers
Figure It Out activities
Number and Algebra
Level Five
Solve multiplication and division problems that involve fractions.
Numeracy activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
solve multiplication and division problems involving decimals
Figure It Out activities
Number and Algebra
Level Five
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10...
solve addition problems using complementary numbers solve subtraction problems using complementary numbers explore complementary numbers in base 2 explore how computers solve mathematical operations
Secondary activities
Number and Algebra
Level Five
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
use a calculator to multiply and divide decimals
Figure It Out activities
Number and Algebra
Level Five
These exercises and activities are for students to use independently of the teacher to practice number and measurement skills.
Design and use models to solve measuring problems in practical contexts.
Secondary activities
Number and Algebra
Level Five
Solve multiplication and division problems that involve fractions.
Numeracy activities
Number and Algebra
Level Five
Estimate and find percentages of whole number and decimal amounts.
Numeracy activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
solve decimal multiplication problems by using compatible numbers solve fraction multiplication problems by using compatible numbers
Figure It Out activities
Number and Algebra
Level Five
These exercises and activities are for students to use independently of the teacher to practice number properties.
solve decimal multiplication problems using place value solve 2 digit by 2 digit multiplication problems using place value solve decimal by 2 digit whole number multiplication problems using place value solve decimal by decimal multiplication problems using place value
Secondary activities
Number and Algebra
Level Four
These exercises and activities are for students to use independently of the teacher to practice number properties
solve problems using doubling and halving, and other proportional adjustments
Secondary activities
Number and Algebra
Level Five
The purpose of this activity is to engage students in recognising patterns in recurring decimals, and linking the size of those decimals to the division of 100 that produces them.
Rich learning activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
solve problems that involve finding and comparing percentages
Figure It Out activities
Number and Algebra
Level Five
learning how to divide a fraction by a fraction
Numeracy activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
solve multiplication and division problems with decimals
Figure It Out activities
Number and Algebra
Level Five
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.
multiply and divide decimals solve currency exchange rate problems
Figure It Out activities
Number and Algebra
Level Five
This unit has a brief look at what is known about Egyptian Fractions. These are unit fractions – fractions whose numerator is one. We look at how fractions can be represented in terms of Egyptian Fractions. Finally we suggest a web site that students might like to use as resource material for a...
add and subtract fractions look for patterns and make conjectures consider infinity in a new situation
Units of Work
Number and Algebra
Level Five
This unit has a brief look at what is known about Egyptian Fractions. These are unit fractions – fractions whose numerator is one. We look at how fractions can be represented in terms of Egyptian Fractions. Finally we suggest a web site that students might like to use as resource material for a...
add and subtract fractions look for patterns and generalise with algebra consider infinity in a new situation.
Units of Work
Number and Algebra
Level Five
The purpose of this task is to engage students in expressing a percentage as a fraction and to be able to apply this as a multiplier.
Rich learning activities
Number and Algebra
Level Five
Solve multiplication and division problems that involve decimals.
Numeracy activities
Number and Algebra
Level Five
Solve multiplication and division problems that involve decimals.
Numeracy activities
Number and Algebra
Level Five
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
find fractions of fractions
Figure It Out activities
Number and Algebra
Level Five