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Finding rules and describing patternsLearning objective

To solve a problem by finding a rule and describing the pattern.

Links to year 2 problem solving and reasoning pupil target sheet

Finding rules and describing patterns

I can work with others to describe the rule of the sequence involving numbers or shapes.

I can work with others to test if the rule works for other predicted terms in the sequence.

I can work with others to continue the sequence.

Teaching notes

• When solving problems of this type, pupils need to look carefully to find a rule and begin to describe the pattern.

• It is important to define the meaning of a ‘pattern’ or ‘sequence’ and a ‘term’. Establish that a pattern or sequence is an arrangement of numbers, lines or shapes that follow a rule.

• When looking for rules and patterns, give pupils access to number lines, 100 squares and other concrete resources that may be useful in helping them spot the pattern.

Example 1: Aunty Mae is knitting a scarf. She started on Saturday and knitted 7cm. She then knitted 10cm each day. On what day of the week was the scarf 67cm long?

• Share the problem with the pupils. Ask: Can you explain what we have to do to solve this problem? – Establish that we need to work out on what day of the week the scarf was

67cm in length.• Represent the problem visually.

– Hold a piece of string up and label it ‘Saturday – 7cm’. – Hold up another, much longer piece of string and label it ‘? – 67cm’. – Explain that we need to find out what day of the week the scarf is at the

length of the longer piece of string.• Ask:

– How long was the scarf on Saturday? – How many centimetres does Aunty Mae knit each day? – What will the length of the scarf be on Sunday?

• Confirm that on Saturday the length of the scarf is 7cm and Aunty Mae will knit 10cm each day. Therefore, the scarf will be 10cm longer on Sunday than it was on Saturday: 7cm + 10cm = 17cm.

• Model how to record this using a table.

Day of the week

Sat Sun

Total length of scarf

7cm 17cm

• Remind the pupils that since Aunty Mae knits 10cm each day, they need to add 10cm to the length of the previous day until they reach 67cm.

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• Give pupils physical resources to help with this as appropriate, e.g. blocks, string, measuring tool and/or a 100 square.

• Ask: What do you notice about the pattern?

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

– Establish by looking at the 100 square that, when adding 10, the digit in the ones column (7) stays the same but the value of the tens digit increases.

• Use this pattern to complete the table:

Day of the week

Sat Sun Mon Tue Wed Thurs Fri

Total length of scarf

7cm 17cm 27cm 37cm 47cm 57cm 67cm

– Establish the scarf will be 67cm in length on Friday.

Example 2: Complete the next two shapes with numbers in this sequence:

14 24 64 7434 44 54 84 94

• Share the problem with the pupils. Ask: Can you spot a pattern for the shapes by simply looking at the sequence?

• Establish that the pattern is made up of stars and circles.• Ask:

– How many circles are there before the next star?

14 24 64 7434 44 54 84 94

Finding rules and describing patterns

18 © 2017 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.

Real-life word problems Learning objective

To solve ‘real-life’ multi-step word problems involving money, time and measures.

Links to year 2 problem solving and reasoning pupil target sheet

Real-life word problems

I can solve simple problems involving money, e.g. combining amounts to make a particular value; giving change.

I can solve simple problems involving time, e.g. sequencing intervals of time.

I can solve simple problems involving mass.

I can solve simple problems involving length.

I can solve simple problems involving capacity.

Teaching notes

• Being able to solve real-life word problems involving money and measures is an important everyday life skill. • When solving word problems, agree the key stages for working through the problem systematically:

– read the question – highlight key words – choose the operation(s) – estimate an answer – calculate – give answer using correct units – check

Example: Sam has £2. He buys 2 giant lollipops. How much money does he have left?

• Share the problem with the pupils. Ask: – What are the key parts of the problem to highlight? – How many steps are there to the problem? – What operation will we need to use to solve the problem? Do we need to use more than one

operation? – Can we make an estimated answer before solving the calculation?

• Model how to solve the problem. – Identify the key words to the problem and highlight them.

Sam has £2. He buys 2 giant lollipops. How much money does he have left?

– Demonstrate how to estimate an answer.• Establish that we need to find the cost of 2 lollipops and then find how much is left from £2.• Work out the cost of 2 lollipops: 55p + 55p. Model different strategies for this calculation, e.g. 50p + 50p = £1; 5p + 5p = 10p; £1 + 10p = £1.10.• Work out the change from £2. Model how to count on to find the change: + 10p + 10p + 10p + 10p + 10p + 10p + 10p +10p + 10p = 90p

£1.10 £1.20 £1.30 £1.40 £1.50 £1.60 £1.70 £1.80 £1.90 £2

55p

55p

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Real-life word problems For pupils – Steps to success

1. Read the problem.

2. Highlight key pieces of information.

3. Identify the operation(s) and order of steps.

4. Estimate the answer.

5. Solve the calculation(s).

6. Check the answer against your estimate.

Bank of ‘Real-life word problems’

1 What is the cost of 2 packs of crisps at 32p per pack?

2 There are 30 children playing football. They get into teams of 5. How many teams are there?

3 Here is a jug of orange juice. Sarah pours 150 millilitres of juice out of this jug.

How much juice is left in the jug?

4 30 blue pens are put into packs of 10.

15 red pens are put into packs of 5.

8 black pens are put into packs of 2.

How many packs are there all together?

5 How many small bottles of water will fill the larger bottle?

100200

300400500

millilitres

12 litre 8 litres

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Measures 1

Example: Write <, > or = in the circles to compare the measures.

5m < 7m 15cm > 9cm

10kg = 10kg 23°C > 17°C

You can measure lengths, masses, volumes, capacities and

temperatures.

You can use symbols to compare measures:

< means ‘is less than’

> means ‘is greater than’

= means ‘is the same as’

Getting started

1 Write true or false for each statement.

a) 3kg > 1kg b) 2kg < 5kg c) 4kg > 5kg d) 3kg < 1kg

2 Taj has three parcels.

4kg 7kg ?

Parcel A Parcel B Parcel C

Parcel A < Parcel C and Parcel B > Parcel C

Use the information about the masses to write down a

possible mass for Parcel B.

How did you do?55

Challenge 1

Challenge 2

3 Is each statement true or false?

a) 5kg < 5kg

c) 6cm = 6m

e) 8m > 1m

b) 7 litres < 5 litres

d) 15°C < 20°C

f) 70mL < 7mL

4 Ned writes two comparisons.

What could the missing numbers be?

a) < 6kg b) = 4m

5 Here are four identical jugs. They each contain some water.

Write down all the different ways to compare the amounts

of water in the jugs.

Jug A Jug B Jug C Jug D

> > >

> > >

6 Use <, > or = to compare the masses of the boxes.

a) Box A Box B

b) Box C Box A

c) Box A Box B + Box C

A

B

C