Representing - Lower Secondary

Representing is part of our Thinking Mathematically collection.

Gender Balance

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 36 - 2012
Can you work out how many more boys are in group 1 than girls are in group 2?

Starting Fibonacci

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 40 - 2012
What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

Bike Shop

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 8 - 2013
If I walk to the bike shop, but then cycle back, what is my average speed?

Odds and Evens

Stage: 3 and 4 Challenge Level: Challenge Level:1

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Revolutions

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 30 - 2006
Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

Searching for Mean(ing)

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Vector Walk

Stage: 4 and 5 Challenge Level: Challenge Level:1

Starting with two basic vector steps, which destinations can you reach on a vector walk?

17s and 23s

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 22 - 2010
Can you form this 2010-digit number...

Don't Be Late

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 31 - 2010
Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Pyramidal N-gon

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 43 - 2014
The base of a pyramid has n edges. What is the difference between the number of edges the pyramid has and the number of faces the pyramid has?

Shilling Tuppence

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 50 - 2014
Cheryl finds a bag of coins. Can you work out how many more 5p coins than 2p coins are in the bag?

Product and Sum

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 7 - 2015
When Jim rolled some dice, the scores had the same product and sum. How many dice did Jim roll?

Oldest and Youngest

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 11 - 2017
Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

Helen's Family

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 42 - 2017
Helen has twice as many sisters as brothers. Her brother Tim has three times as many sisters as brothers. How many children are there in the family?

Doubly Consecutive Sums

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 51 - 2017
How many numbers less than 2017 are both the sum of two consecutive integers and the sum of five consecutive integers?