nz maths place value problem solving

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E: Learning to understand and use place value to solve problems

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Target group:  Students in years 3–6

Focusing on:

• creating models of whole numbers using place value materials
• ordering three-digit numbers
• using place value partitioning as a strategy to solve addition and subtraction problems.

Teacher observation over a range of activities

The student may have rote-learned place value names and may be able to identify the digit in the tens or hundreds place but cannot create a model of whole numbers. The student may not understand 10 as the basis of our number system and may see 1 purely as a counting unit.

Possible barriers to the student’s progress

• Limited understanding of place value notation
• Difficulty visualising place value groupings
• Limited understanding of groupings of ten

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Resources tagged with: Place value

There are 133 NRICH Mathematical resources connected to Place value , you may find related items under Place value and the number system .

The Number Jumbler

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Digit Addition

Try out this number trick. What happens with different starting numbers? What do you notice?

Dicey Operations in Line

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Dicey Addition

Who said that adding couldn't be fun?

Where should you start, if you want to finish back where you started?

Forwards Add Backwards

What happens when you add a three digit number to its reverse?

By selecting digits for an addition grid, what targets can you make?

Subtraction Surprise

Try out some calculations. Are you surprised by the results?

Multiply Multiples 3

Have a go at balancing this equation. Can you find different ways of doing it?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Round the Three Dice

What happens when you round these three-digit numbers to the nearest 100?

Round the Dice Decimals 2

What happens when you round these numbers to the nearest whole number?

Multiply Multiples 2

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Two Spinners

What two-digit numbers can you make with these two dice? What can't you make?

Snail One Hundred

In this game, you throw a dice and move counters along the snail's body and in a spiral around the snail's shell. It is about understanding tens and ones.

That Number Square

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Always a Multiple?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Our Numbers

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Dicey Operations

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Coded Hundred Square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Two-digit Targets

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Four-digit Targets

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Method in Multiplying Madness?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

An Easy Way to Multiply by 10?

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Can you replace the letters with numbers? Is there only one solution in each case?

Sixty-seven Squared

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

Six Times Five

How many six digit numbers are there which DO NOT contain a 5?

Which Is Quicker?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Think of Two Numbers

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Number Rules - OK

Can you produce convincing arguments that a selection of statements about numbers are true?

Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Which Scripts?

There are six numbers written in five different scripts. Can you sort out which is which?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Legs Eleven

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Number Detective

Follow the clues to find the mystery number.

Writing Digits

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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• Comparing and ordering decimals
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• Dividing decimals
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• Range, variation and standard deviation
• All about angles
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• The Pythagorean Theorem
• Introduction to sine, cosine and tangent
• Find an unknown side length
• Find an unknown angle measure
• Using trig in the real world

PLACE VALUE

In this module, you can study the concept of place value and have an introduction to the decimal number system.  Also included on this page are the concepts of expanded form and word form of decimal numbers.

Did you know?

Digits to the left of the decimal point represent whole numbers; digits to the right of the decimal point represent parts or fractions of numbers.

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• Fourth Grade

Place Value Problems

Fourth grade place value problems.

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