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8 warm-up maths challenges to use in the classroom

Looking for an opportunity to practise problem-solving strategies with your students? Use some of these fun warm-up challenges in your classroom and see how your students fare!

Lower Years

Challenge 1

Gabby is making snack boxes for a picnic. She has yoghurt cups, apples and biscuits. Each snack box gets 2 different items. How many different combinations of snack boxes can Gabby make?

Try the strategy: Making an organised list

Answer: 3 different combinations
apple and biscuit
apple and yoghurt cup
biscuit and yoghurt cup

Challenge 2

Ben, Indy and Nour took turns skip counting by 5s.
Ben went first, then Indy, then Nour.

They started with 5 and finished on 100.

Who said the last number?

Try the strategy: Acting it out or Finding a pattern or rule

Answer: Indy

Ben	Indy	Nour
5	10	15
20	25	30
35	40	45
50	55	60
65	70	75
80	85	90
95	100

Challenge 3

Nick used a method to turn words into numbers by giving letters of the alphabet a value.
BEE = 12
BUG = 30
What would FLY be?

Try the strategy: Guessing and checking or Finding a pattern or using a rule

Answer: 43
Numbering the alphabet letters in order from A–Z results in:

B + E + E = 2 + 5 + 5
= 12

and
B + U + G = 2 + 21 + 7
= 30

Therefore: F + L + Y = 6 + 12 + 25
= 43

Upper Years

Challenge 4

If the name Matilda is written repetitively (like this: MATILDAMATILDAMATILDA), what is the 50th letter?

Try the strategy: Finding a pattern or using a rule

Answer: M
The pattern repeats every 7 letters, so the name ends on the 7th, 14th, 21st letters and so on (i.e. on every multiple of 7).

Following the pattern, the 49th letter will be the end of MATILDA (written 7 times over), so the next letter will be M.

This means the 49th letter is A and the 50th letter is M.

Challenge 5

A kite is 12 m above a lake. It drops 4 m, then rises 2 m, then drops 4 m, then rises 2 m, and so on. How many drops until the kite touches the water?

Try the strategy: Drawing a picture or diagram

Answer: 5 drops

Challenge 6

Trey has three times as many comic books as Hanh. Felix has half as many comic books as Hanh. If Trey has less than 18 books and Hanh has more than 2, how many comic books does each person have?

Try the strategy: Guessing and checking

Answer: Felix = 2, Hanh = 4, Trey = 12
Trey has three times as many as Hanh.
Felix has half as many as Hanh.

Challenge 7

A kangaroo is hopping along the beach leaving tracks in the sand. Each hop is 7 m long. How many tracks will the kangaroo leave in 150 m?

Try the strategy: Drawing a picture or diagram or Finding a pattern or using a rule

Answer: 22 tracks
The kangaroo hops 10 times in 70 m, 20 times in 140 m and 21 times in 147 m.
21 hops leaves 21 tracks, plus one more for the kangaroo’s starting position.

Challenge 8

Jarrah has 8 tins of paint in different colours. He creates new colour blends by mixing small quantities of 2 colours together. How many different colour blends can Jarrah make?

Try the strategy: Solving a simpler problem

Answer: 28
Look for a pattern by listing colour blends for 4 tins of paint (A, B, C, D):

AB, AC, AD
BC, BD
CD

Total colour blends for 4 tins = 3 + 2 + 1
= 6

Use the same pattern for 8 tins:
Combinations for 8 tins = 7 + 6 + 5 + 4 + 3 + 2 + 1
= 28