Level Four > Number and Algebra

AO1: Use a range of multiplicative strategies when operating on whole numbers.

Children

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Multiple Ways to Add and Subtract

Use multiplication to solve addition and subtraction problems.

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Common Multiples

This activity provides students with a fun, game context in which to practice finding common multiples of numbers. Ths activity build knowledge tohelp develop multiplicative strategies.

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Factor Cards

This activity provides students with a fun, game context in which to practice their factorisation skills. This activity builds the knowledge to help develop multiplicative strategies.

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This is to That

In this unit we look at ratio, what it means for numbers or objects to be in a given ratio, and how ratios and fractions are related.

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This unit is designed to provide students with a measurement context in which to use number operations. In calculating speed from distance and time, they will apply number strategies as they convert between units.

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Eights

Multiply large numbers by 8

Find and describe patterns in numbers

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Create A Question

Use their mathematical knowledge to invent problems

Solve other students' problems.

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5c and 9c Stamps

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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4c and 7c Stamps

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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Dartboards

Identify and describe patterns in numbers..

Devise and use problem solving strategies to explore situations mathematically (be systematic).

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More Dartboards

Identify and describe patterns in numbers

Work systematically to find the possible outcomes

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The Escape

Find strategies for investigating number problems;

Find a common multiple of a group numbers.

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The Multiplier (2-digit by 2-digit numbers)

This unit uses The Multiplier, one of the digital learning objects that can be found in Te Pataka Matihiko, Our Digital Storehouse, to multiply 2-digit numbers by 2-digit numbers. It is designed for students working at Stage 7-Advanced Multiplicative of the Number Framework and is the third in a series of four units that focus on using the Multiplier as an aid to learning multiplication.

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The Multiplier (origin of the algorithm)

This unit uses The Multiplier, one of the digital learning objects that can be found in Te Pataka Matihiko, Our Digital Storehouse, to multiply 2-digit numbers by 2-digit numbers. It is designed for students working at Stage 7-Advanced Multiplicative of the Number Framework and is the fourth in a series of four units that focus on using the Multiplier as an aid to learning multiplication. In this unit, The Multiplier is used as a tool to outline the origins of the standard algorithm for multiplication.

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The divider (mixed number quotients)

This unit uses two of the series of four Divider learning objects to support the students division of whole numbers where the quotient is a mixed number (whole number and fraction). The Divider encourages the students to split a division problem into parts based on known division or multiplication facts. The divider is based on a rectangular representation of division where one of the side lengths is unknown.

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Multiplication and Division Pick n Mix 1

In this unit we look at a range of strategies for solving multiplication and division problems with whole numbers with a view to students anticipating from the structure of a problem which strategies might be best suited. This unit builds on the ideas presented in the Multiplication Smorgasbord session in Book 6: Teaching Multiplication and Divsion.

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Weighty Averages

This unit encourages students to explore ways of working out problems that involve finding the average percentage of the contents of differently sized containers. It is suitable for students working at Stage 7-Advanced Multiplicative of the Number Framework. This unit is a useful introduction to the Level 5 unit: Mix Up 2.

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Mix Up 1

This unit uses one of the digital learning objects, the Mix Up 1, to support students as they investigate finding average percentage of the contents of equally sized containers. It is suitable for students working at Stage 7-Advanced Multiplicative to Stage 8-Advanced Proportional of the Number Framework. It includes problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

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Cut and Paste

Solve multiplication and division problems by using proportional adjustment.

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Doubling and Halving

Solve multiplication and division problems by using proportional adjustment.

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Proportional Packets

Solve multiplication and division problems by using proportional adjustment.

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The Royal Cooking Lessons

Solve multiplication and division problems by using proportional adjustment.

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Remainders

Solve division problems that involve remainders.

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Multiplying by 25

Solve multiplication and division problems by using proportional adjustment.

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Paper Power

Solve multiplication and division problems by using tidy numbers.

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Adding Sequences

Use multiplication to solve addition and subtraction problems.

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Using 0

Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.

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Order of Operations

Use a range of strategies to solve problems that involve a combination of addition, subtraction, multiplication, and division.

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To Turn or Not to Turn

Solve division problems that have fraction answers.

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Divisibility Tests

Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.

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The Equals Sign Again

Solve multiplication and division problems by using proportional adjustment.

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Cross Products

Solve multiplication and division problems by using place value.

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Little Bites at Big Multiplications and Divisions

Solve multiplication and division problems by splitting factors.

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Nines and Threes

Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.

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Introducing Decimal Fraction Place Value

Solve division problems by sharing.

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Finding Remainders

Solve division problems that involve remainders.

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Applying Remainders

Solve division problems that involve remainders.

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Pigeonholes

Solve division problems that involve remainders.

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Multiple Ways to Add and Subtract

These exercises and activities are for students to use independently of the teacher to practise number properties.

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Double Double Boil and Bubble

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation and should be formally written up (Investigation Write Up) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

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Homework sheet: stage 6 – 7 Revision of add-sub and mult-div domains

These exercises and activities are for students to use as a week’s homework to practice number properties

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Homework sheet: stage 6 – 7, Revision of add-sub and mult-div 2

These exercises and activities are for students to use as a week’s homework to practice number properties

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Number in Geometry

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 to 15 minute activity.

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Doubling and halving

These activities are designed to teach doubling and halving strategies.

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Cross Products

These exercises and activities are for students to use independently of the teacher to practice number properties.

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Factor Puzzles

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Trying Times

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Eleventh Heaven

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Napier's Bones

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Matrix

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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How Many Factors?

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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To and Fro

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Fun Rides

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Booked!

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Sweet Thoughts

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Changes, Highs, and Lows

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Division Delights

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Think Tank

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Mystery Hexagons

This is a level 4 number and algebra activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Flying Home

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Oceans Apart

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Food for All

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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The Fish Hooks of Ngāke

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Focusing on Water

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Number Patterns

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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How Many?

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Fun Times

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Divisive Tactics

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Frantic Fund-raising

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Crossing Out Singles

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Cover Up

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Team Leaders

This is a level 3 number link activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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Egyptian Multiplication

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Digit Challenge

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Exploration to Earth

This is a level 3 number link activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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Orchard Antics

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Revisiting Remainders

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Remainder Bingo

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Factorials

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Order of Operations

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Operations Checker

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Plastic Fantastic

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Percentage Passes

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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A Matter of Factor

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Among the Dolphins

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Fair Mix

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Slip-sliding Away

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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What's Best?

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Just Right!

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Branching Out

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Calculation Chains

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Triple Trouble

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Pizza Split

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Horsing Around

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Perfect Lasagne

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Digital Dilemmas

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Fenced In

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Speaking in Riddles

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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The Great Factor Hunt

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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The Factoring Factory

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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What to Do?

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Factor Patterns

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Nimble Numbers

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Aiming High

This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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Birthday Treat

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Keep Your Shirt On

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Division Dilemmas

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Divide and Conquer

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Egging On

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Double Russian

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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High Powered Thinking

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Multiple Methods

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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What a View!

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Multiplication Roundabouts

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Planting with the Whānau

This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.

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Size-wise

These are level 4 number problems from the Figure It Out series.

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Ps for Ever

These are level 4 measurement, number and algebra problems from the Figure It Out series.

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Locomotive Magic

These are level 4 and 5 number problems from the Figure It Out series.

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Stretching Exercises

These are level 4 number and measurement problems from the Figure It Out series.

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Finding a Way

These are level 4 number, and geometry problems from the Figure It Out series.

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Lining Up

These are level 4 number and statistics problems from the Figure It Out series.

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You're All Heart!

These are level 4 number, and measurement problems and level 3 algebra problems from the Figure It Out series.

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What Goes Around ...

use common multiples to solve problems (Problem 1)

use addition and problem solving strategies to solve problems (Problem 2)

continue a sequential pattern to find a rule and predict a future member (Problem 3)

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AO1: Use a range of multiplicative strategies when operating on whole numbers.