Numbers and the number system
Multiples
Solving mathematical problems
Challenge 2
4
6
0
5
10
15
0 1 2 3 4 5 6 7 8 9
Draw this number line. Starting from 0, write all the multiples of 2 above the line. Starting from 0, write all the multiples of 5 below the line. Now add together pairs of numbers that are above and below each other. 4 + 10 = 6 + 15 = 2+5= What do you notice?
Write one 2-digit number in each box. You can only use each digit once in a number.
Smallest 2-digit number
Solving mathematical problems
You will need: • set of 0–9 digit cards (optional) Largest 2-digit number
even number odd number multiple of 2 multiple of 3 multiple of 5 multiple of 10
Think about …
Think about … Think carefully about how you’re going to record the results of adding pairs of numbers that are above and below each other. You need to look out for any patterns.
Keep checking as you count along the line and write down the multiples.
How do you know that a number is a multiple of 2, a multiple of 3, a multiple of 5 or a multiple of 10?
What do you notice about the even numbers and the multiples of 2 you have written in the boxes? Why is this?
What if ?
What if ? What if you find the difference between pairs of numbers that are above and below each other? What do you notice? 10 – 4 =
15 – 6 =
What about adding together and finding the difference between pairs of multiples of 2 and 3? What about adding together and finding the difference between pairs of multiples of 3 and 5? 8
2-digit numbers Challenge g
0
5–2=
Numbers and the number system
Write 2-digit numbers in the boxes. You can only use each digit once in a number. All the numbers between 40 and 50
Number closest to 64
even number odd number
When you’v e finished, tur n to page 80.
multiple of 3 multiple of 5 multiple of 10
When you’v e finished, tur n to page 80. 9
Numbers and the number system
Ordering numbers
Solving mathematical problems
Challenge
Four cubes Challenge
<
34
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Using red and blue interlocking cubes, join four cubes together to make a shape.
38
What numbers could you write on the red card? Write a rule for finding all the numbers that you could write on the red card.
Check your numbers to make sure that they fit the statement.
Or like this?
What about like this? 10
81 67
You will need: • red, blue and green interlocking cubes
Think about …
What if ? What if the cards are arranged like this?
Solving mathematical problems
How many cubes are red? How many are blue? What fraction of your shape is red? What fraction is blue? How many different ways can you make a shape using other combinations of four red and blue cubes? How many cubes are red? Blue? What fraction of your shape is red? Blue?
Think about … There is more than one number: can you find all the possible numbers?
Numbers and the number system
49 > <
>
> < >
Think about using the number of cubes of each colour to help you describe the shapes as fractions.
42
What if ?
50 73
Remember that a fraction can be used to describe part of a group of objects.
When you’v e finished, tur n to page 80.
What if you join four red, blue and green interlocking cubes together to make a shape? How many cubes are red? Blue? Green? When you’v What fraction of your shape is red? Blue? Green? e finished, tur n to page 80.
11
Fraction statements
Numbers and the number system
Solving mathematical problems
Challenge
Showing halves and quarters
Numbers and the number system
Challenge halleng g
2 out of 4, or a half, are wearing glasses.
Solving mathematical problems
You will need: • counters (or similar) • selection of different resources
Here are two different ways of showing half of 12.
How many different fraction statements can you make to describe the people in the picture?
Think about …
What if ? How many other ways can you find to show half of 12?
Use fractions and words such as ‘out of’ to describe what you see in the picture.
Think about … Look around the classroom for different resources you can use.
Think about what is the same and what is different about the people in the picture, and how many of each there are. 12
Think carefully about how you’re going to show your results – you might need to make a diagram or draw a picture.
What statements can you make about this tray of gingerbread? When you’v e finished, tur n to page 80.
What if ? What different ways can you find to show a quarter of 12?
When you’v e finished, tur n to page 80. 13