Patterns and positions

A number pattern has a rule

Read 12, 14, 16, 18. Each number is two more than the one before. Add two again to get 20.

Now read 35, 30, 25, 20. Each number is five less than the one before. Take away five again to get 15. A pattern can go down as well as up.

Do not use only the first two numbers. Check your rule at each step. For 10, 20, 30, 40, adding ten works all the way along.

Check your understanding 1 Keep the same rule

The same step is used each time: 27, 37, 47. Choose add or subtract, give the step size, then write the next two numbers.

Add or subtract?

SubtractCorrectIncorrectAddCorrectIncorrect

Step size

Next number

Following number

Check answer

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Add ten each time: 57, 67. Starting a new rule at the last step would make a different pattern.

An ordinal tells a position

Put five objects in a row. Point to the left end and say, “We start here.” Touch each object and say first, second, third, fourth, fifth.

There are five objects altogether, but one object is fifth. Five tells how many. Fifth tells a position.

Turn around and start counting from the right end. The first object changes. Always say where the line starts.

Third and 3rd name the same position. Three and 3 tell how many. First is 1st, second is 2nd and third is 3rd. From fourth to tenth, the symbols end in th: 4th, 5th, 6th, 7th, 8th, 9th, 10th.

Check your understanding 2 Where does the line start?

Five cards lie in this order from left to right: A, B, C, D, E. Which card is second from the right? Which is second from the left?

Second from the right

Select an answerCard CCard ECard BCard ACard D

1. Card C
2. Card E
3. Card B
4. Card A
5. Card D

Second from the left

Select an answerCard ACard DCard BCard ECard C

1. Card A
2. Card D
3. Card B
4. Card E
5. Card C

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D is second from the right. B is second from the left. Counting from the other end changes the starting card, so it can change the answer. D is fourth from the left: A, B, C, D.

Check your understanding 3 One position, two ways to write it

Ten cards lie in this left-to-right order: D, A, H, C, F, B, J, E, I, G. Count from the right. What is card D’s position? Give its word and its symbol. The cards do not have to be in alphabet order: use the order given.

Card D's position from the right, in words

Select an answerthirdsixthfirsteighthfourthfifthtenthninthseventhsecond

1. third
2. sixth
3. first
4. eighth
5. fourth
6. fifth
7. tenth
8. ninth
9. seventh
10. second

Card D's position from the right, in symbols

Select an answer2nd3rd10th1st5th8th6th7th4th9th

1. 2nd
2. 3rd
3. 10th
4. 1st
5. 5th
6. 8th
7. 6th
8. 7th
9. 4th
10. 9th

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Card D is tenth, written 10th, from the right. From the left it would be first, 1st. There are still ten cards altogether whichever end you start from.

Make your own

Write a number pattern with four numbers below 100. Ask someone to find its rule. Then line up ten small objects and point to the third, seventh and tenth from your chosen start.