a selection of maths problems for year 4

©AJW 2014

A Selection of Maths

Problems for Year 4

© AWE 2012 www.spearmaths.co.uk

D18

Objectives

Use drawings or resources to help visualise the problem

Use a systematic approach to solve the problem

Choose and use an appropriate method of recording

Try other possibilities to test the solution

Polygon Hunt

On a 3 x 3 pinboard, how many different triangles can you make?

Different means no ‘flip overs’ or ‘turn rounds’

How many different quadrilaterals can you make on a 3 x 3

pinboard? What about pentagons? Hexagons? Heptagons?

Can you make an octagon on a 3 x 3 pinboard?

These triangles

are all the same

These triangles

are different


Answer to D18 Polygon Hunt

These are the 8 triangles you can make.

You can make:

8 different triangles

16 different quadrilaterals

23 different pentagons

22 different hexagons

5 different heptagons

It is impossible to make an octagon on a 3x3 pinboard


K x A = DF

F x A = BD

D x A = H

E x A = BE

J x A = DG

H x A = BK

B x A = A

G x A = DB

BC x A = AC

BD x A = AH

BB x A = AA

A x A = J

L28

Objectives Recognise simple patterns or relationships, generalise and predict

Suggest extensions by asking ‘what if…?’ or ‘what could I try next?’ Look for any relationships and patterns in the information given Use recording to make sense of the information given and to find

missing information

Check that the answer meets all of the criteria

K x A

Each letter (in the equations

on the left of the page)

stands for a single digit.

Where there are two letters

next to each other, this

stands for a two-digit number.

Each letter stands for the

same digit throughout all the

equations.

Can you work out what digit

each letter stands for?

Hint: You don’t have to start

at the top!


Answer to L28 K x A

A=3

B=1

C=0

D=2

E=5

F=4

G=7

H=6

J=9

K=8

NB: There is no ‘I’ in the list as this may look too much like a ‘1’


P100

Objectives Recognise patterns or relationships

Generalise and predict Suggest extensions by asking ‘what if…?’ or ‘what could I try next?’ Organise the recording of possibilities eg in an ordered list or table

Have a system for finding the possibilities eg start with the smallest number, know when all possibilities are found, check for repeats of possibilities

Sheep and Chickens +

Simon looked at the sheep and chickens in a field.

He counted 28 legs.

How many sheep and chickens could there be?

Find as many ways to do it as you can.

Show your thinking.


Answer to P100 Sheep and Chickens +

0 + 28 0 sheep, 14 chickens: doesn’t really count as it doesn’t include any sheep

4 + 24 1 sheep, 12 chickens






28 + 0 7 sheep, 0 chickens: doesn’t really count as it doesn’t include any chickens


R23

Objectives

Recognise and explain patterns or relationships, generalise and

predict

Describe and extend simple number sequences


Choose and use an appropriate method of recording

3 Consecutive Numbers

Consecutive numbers are whole numbers that follow each other

without gaps: 1, 2 and 3 are consecutive; 2, 3 and 7 aren’t.

Find three consecutive numbers that add up to 39

What other numbers up to 50 can you make by adding three

consecutive numbers?

Look for a pattern.

What is the pattern of numbers you can make by adding four

consecutive numbers?


Answer to R23 3 Consecutive Numbers

1 + 2 + 3 = 6

2 + 3 + 4 = 9

3 + 4 + 5 = 12

4 + 5 + 6 = 15

5 + 6 + 7 = 16 etc.

The sum of three consecutive numbers = 3 x the ‘middle’ number, so all the answers are

in the 3 x table (ie 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48)

12 + 13 +14 =39

4 Consecutive numbers:

1 + 2 + 3 + 4 = 10

2 + 3 + 4 + 5 = 14

3 + 4 + 5 + 6 = 18 and so on going up in 4s


W22

Objectives

Choose and use appropriate number operations and appropriate

ways of calculating to solve problems


Use all four operations to solve word problems involving

numbers in ‘real life’

1, 2, 3 and 4 make…

Use only the digits 1, 2, 3, and 4 (one of each).

You can also use any operations you like: + - x ÷ as many

times as you like

Here is a calculation that totals 1: 2 + 3 – 4 x 1 = 1

Here is a calculation that totals 40: 43 – 2 – 1 = 40

Now make up calculations that total 2, 3, 4, 5, 6, 7 etc.

Can you make each number

from 1 to 40?

Create a way to work systematically.


Answer to W22 1, 2, 3 and 4 make…

2 + 3 – 4 x 1 = 1

2 + 3 – 4 + 1 = 2

4 + 2 – 3 x 1 = 3

4 + 2 + 1 – 3 = 4

4 + 3 – 2 x 1 = 5 etc.

It is possible to make all the numbers from 1 to 40 eg 43 – 2 - 1 = 40

a selection of maths problems for year 4

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