Addition Strips

Introduction

Addition Strips are made by drawing a row of boxes, filling in two numbers in the first two boxes, and then using addition to complete the rest of the boxes. Look at the example on the right, it shows you how to do that. Addition Strips can be any length, as long as there are at least three boxes. The one on the right is a Size 5 Addition Strip because there are 5 boxes in total.

Have a go at the questions below:

Generalising

For a Size 5 Addition Strip, can you come up with a rule of how to find out the last number given the first and second numbers WITHOUT finding the third and fourth numbers?

Use your rule to find out what the last number is given the first number is 3 and the second number is 10. (Do NOT find the third and fourth numbers!)

Now verify that your rule indeed works by finding the middle numbers and completing the addition strip.

Use your rule to find out what the first number is given the second number is 4 and the last number is 26. (Do NOT find the third and fourth numbers!)

Now verify that your rule indeed works by finding the middle numbers and completing the addition strip.

Now practise by attempting the two worksheets below:

Number Strips - Problems.pdf

Number Cells.pdf

Further Questions and Challenges

Part 1

What happens if the first two numbers are the same?
What can you say about the total?
Can you explain why this happens?

Part 2

What happens if the second number is twice as big as the first?
What can you say about the total?
Can you explain why this happens?

Part 3

What happens if the first number is twice as big as the second?
What can you say about the total?
Can you explain why this happens?

Part 4

What rule would mean that the totals are always multiples of 11 (in the 11 times table)?
Try to find to rules for this to work.
What is the next type of total that can be made in two different ways?
What’s the smallest type of total that can be made in three different ways?

Part 5

Now try some more rules or the starting numbers and see if you can make a statement about the totals that they give. Try these rules to start with:

The second number is one more than the first
The second number is two more than the first
The second number is one less than the first

Part 6

Look at the two-way table on the right. This is another way to record your answers.

Can you work out what goes in spaces?
Complete the table, can any spot interesting pattern?

Part 7

Repeat the above parts with different sized Addition Strips.

Extension

While it is not required at Year 7, some basic understanding of algebra may help you to simply and solve the problems above. You may wish to take a look at topics such as "substitution", "collecting like terms", "forming expressions" and "solving equations". The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.

Now see if you can apply what you have learnt with algebra to solve the following Addition Strips problems:

Strips.pdf

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