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NA4-1: Use a range of multiplicative strategies when operating on whole numbers.

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Elaboration on this Achievement Objective

This means students will apply the properties of multiplication and division (commutative, distributive, associative and inverse) to number problems, particularly those requiring multiplication and division. Students should exercise critical choice in their method of calculation - mental, machine or paper - and recognise situations in which estimation should be used, including the checking of calculated answers. Strategies expected at Level Four include: using common factors and multiples, for example 37 + 41 + 40 + 38 = box. as 4 x 40 – 4, using the distributive property, for example 24 x 36 = 20 x 36 + 4 x 36, 9 x 78 = 9 x 80 – 9 x 2, or 276 ÷ 12 = 240 ÷ 12 + 36 ÷ 12, using the associative property, for example 12 x 33 = 4 x 99, or 216 ÷ 12 = 216 ÷ 2 ÷ 2 ÷ 3, and inverse operations (reversing), for example 354 ÷ 6 = box. as 6 x box. = 354. This objective also involves calculating powers, for example 43 = 4 x 4 x 4 = 64, and factorials, for example 4! = 1 x 2 x 3 x 4 = 24. Students should have strong mental strategies for operations on whole numbers but also accurately carry out standard written algorithms, particularly for multi-digit multiplication and division. Level Four corresponds to the Advanced Multiplicative stage of the number framework.

 

Teaching resources for this Achievement Objective
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$4 and $7 Stamps

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Describe what it means for a sequence to carry on infinitely.
  • Look for patterns using linear combinations of 4 and 7.
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$5 and $9 Stamps

Level Four
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Describe what it means for a sequence to carry on infinitely.
  • Look for patterns in linear combinations of numbers.
  • Devise and use problem solving strategies (guess and check, make a table, look for patterns).
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Across Lake Taupō

Level Four
Integrated
Rich learning activities
The purpose of this activity is to engage students in using multiplicative and/or additive strategies to solve a measurement problem.
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Adding Sequences

Level Four
Number and Algebra
Numeracy activities

Use multiplication to solve addition and subtraction problems.

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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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Adventure Tokens

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.

choose from a variety of mental strategies to solve problems

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Aiming High

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

use place value strategies to solve addition problems

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A Matter of Factor

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 factors of numbers

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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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Among the Dolphins

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 a variety of strategies to solve problems

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Anno’s Mysterious Multiplying Jar

Level Four
Number and Algebra
Picture book activities
This is an activity based on the picture book Anno’s Mysterious Multiplying Jar. This book may no longer be available for purchase.
  1. Students will construct model to illustrate their understanding of factorials.
  2. Students will be able to explain the power of the operation of multiplication and contrast it with addition.
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Applying Remainders

Level Four
Number and Algebra
Numeracy activities

Solve division problems that involve remainders.

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A Prime Search

Level Four
Number and Algebra
Units of Work
In this unit we use rectangular models or arrays to explore numbers from one to fifty. We systematically identify all the factors of numbers, and are introduced to prime numbers.
  • Model the numbers from 1 to 100 as rectangular arrays.
  • Connect the possible arrays for a given number to the factors of that number.
  • Identify the factors of the numbers 1 to 100 using divisibility.
  • Identify whether natural numbers from 1 to 100 are prime, composite, or a special case (i.e. 1).
  • Calculate300
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Average Ability

Level Four
Number and Algebra
Numeracy activities

Use multiplication to solve addition and subtraction problems.

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Bean Counters

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 tidy numbers to solve multiplication problems

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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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Birthday Treat

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.

sovle problems involving addition, subtraction, multiplication and division of money

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Booked!

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.

solve money problems involving  multiplication and division

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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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Calculation Chains

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 place value knowledge to check calculations

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Car number plates

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in applying place value and combinations to work out the number of possible number plates.
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Car number plates

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in applying place value and combinations to work out the number of possible number plates.
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Cats and bods

Level Four
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in solving a problem involving the multiplicative strategies that form the basis of early algebraic investigation.
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Changes, Highs, and Lows

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 using place value knowledge whole numbers and decimals