e.3.1 describe a puzzle or problem using numbers, practical materials and diagrams

8/7/2019 E.3.1 Describe a Puzzle or Problem Using Numbers, Practical Materials and Diagrams

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Describe a puzzle or problem using numbers, practical materials and diagrams; use these to solve the problemand set the solution in the original context

(Objective repeated in Block E Units 1, 2 & 3)

• Sit children in a circle and lay out the floor dominoes on the carpet (alternatively spread lots of dominoes on the carpet in front of groups of children).

Ask the children to find all the dominoes with a total of six spots.

When all the dominoes with six spots have been sorted, move the other dominoes to one side.

• Say that you are going to check their counting. Select the domino with four spots on the left and two on the right.

Q Look at this domino. How many spots does it have on this side?

Q How many on this side?

Q So how many spots altogether?

Write the number sentence on the board, 4 + 2 = 6, saying 4 add 2 equals 6 altogether. Draw the domino above the sentence. Now turn the domino round sothat the two spots are on the left.

Q What number sentence can we write now? Is it the same as before?

Write the number sentence on the board, 2 + 4 = 6, saying 2 add 4 equals 6 altogether.

Stress that it does not matter which way we add the two numbers we will still get the same total.

• Repeat for 1 + 5 and 5 + 1 and 0 + 6 and 6 + 0. Ask children to write the number sentences on the board.

• Ask children to work in pairs to find all the dominoes with a total of seven spots on their table and to record them by drawing them on Activity sheet Y1 1.As you work with different groups of chi ldren encourage them to say and write the number sentences to go with the dominoes.

When children are confident, ask them to write the number sentences next to the dominoes.

Repeat asking the children to find all the dominoes with eight spots.

Present Resource sheet Y1 2 “The Toy Shop” to the class and read together the names of the toys. Clap or tap on a drum the value of each item.

Which toy is the most expensive?

Establish that the car is the most expensive as 10p has the highest value. Refer to class number line.

Which toy is the cheapest?

Establish that the ball is the cheapest as 3p has the lowest value. Refer to class number line.

Which toy costs more the train or the doll?

Ask the children to explain how they worked out their answers. Emphasise that if the train costs more than the doll the train is more expensive.

How much more was the train than the doll?Use a number line to demonstrate counting on to find how much more.

If the train costs more than the doll what could we say about the doll?

Establish that as the doll costs less than the train the doll is cheaper.Repeat using different examples from “The Toy Shop.”Using laminated cards ask the children to put the toys in order starting with the lowest value.

Using laminated cards of Resource sheet Y1 2, put one of the cards into a bag making sure the children can still see Resource sheet Y1 2.Tell the children that you have one of the toys in the bag and they have to ask questions to work out which toy is hidden. Encourage the chi ldren to askquestions such as:

Is the toy in the bag worth more/less than the train?

Is it 5p more than the ball?

Refer the children to Resource sheet Y1 2. Tell them that they are going to buy two of the toys. Working in pairs, they can choose which toys they want andcalculate out how much it will cost.Give the children a few minutes to record their answers on their whiteboards. Ask some of the children to feedback to the whole group and explain how theyworked out their answers.Model the calculations on the whiteboard using + and = in a number sentence. Make sure the examples you select are not the ones for the next activity.Tell the children that they are going to be set a challenge.

Can they choose the two toys which, when totalled together would cost the most? What is the total cost?

Establish that it is the car and the boat. Model the calculation on the whiteboard.

Which two toys would cost the least? What is the total cost?

Establish that it is the ….and the ……. Model the calculation on the whiteboard.

Ask the children:

How much would it cost if we bought two trains? What do we need to know to work the answer out as quickly as possible?

Make sure the children understand that they can apply their knowledge of doubling to work out the answers for all the toys.

Show Resource sheet Y1 3 of a bus with 20 windows.

Say that 8 people will be getting on the bus. Show the 8 counters to represent people. Invite a child to come and arrange the counters on the bus.

Q How many people has Rebecca put on the top deck of the bus? How many people has she put on the lower deck? So how many people altogether?

Say, '6 on the lower deck, add on 2 more is 8'. Model holding up 6 fingers and counting on from 6 saying ‘7, 8’. Model the addition on a number line. Start on6 and jump on 2.

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Write on board 8 = 6 + 2.

Invite another child to rearrange the 8 counters, saying that you and the class are going to try and find different ways of arranging the 8 people.

Q How many people has Nazeem put on the top deck? (5) How many on the bottom? (3) How can we check that there are still 8 people on the bus?

Point to the five on the lower deck, hold up three fingers, saying ‘three more people, six, seven, eight’.

Q If I put my finger on 5 on the number line and jump on 3 what number will I land on?

Ask the children to look at the number line and invite a child to come and start on 5 and jump on 3.

Write on the board 8 = 5 + 3.

Repeat the process for other arrangements.

Give each child a copy of Resource sheet Y1 3 and 10 counters. Ask them to arrange the 10 counters on the bus in different ways and to write each differentway as a number sentence in their books.

Make Resource sheet Y1 3 into an OHT.

Show OHT of bus. Put 7 counters on the bus to represent people.

Q How many people are on the bus?

Ask children to hold up that number of fingers.

Say that 2 people want to get off the bus at the next bus stop.

Q How many people will be left on the bus?

Encourage children to use their fingers to find out by holding up 7 fingers and bending down (taking away) 2 of their fingers. Model how to do this by saying,‘7 take way 1 is 6’ (as you bend down 1 finger) ‘take away 2 is 5’ (as you bend down the second finger).

On the OHT repeat the process, taking 1 counter away at a time and saying, ‘7 take away 1 is 6, take away 2 is 5’.

Write on the board: 7 take away 2 is 5.

Invite a child to come and write the number sentence on the board using the symbols – and = i .e. 7 – 2 = 5.

Put 10 counters on the bus.

Q How many counters on the bus?

Ask children to hold up that number of fingers.

Say that 4 people want to get off the bus at the next bus stop.

QThere are 10 people on the bus but 4 people want to get off. How many people will be left on the bus?Encourage children to use their fingers to find out by bending down (taking away) 4 of their fingers. Model how to do this by saying, ‘10 take way 1 is 9 (as you

bend down 1 finger) take away 2 is 8 (as you bend down the second finger) take away 3 is 7, take away 4 is 6’.

On the OHT repeat the process, taking 1 counter away at a time and saying, ‘10 take away 1 is 9, take away 2 is 8, take away 3 is 7, take away 4 is 6’.

Write on board 10 take away 4 is 6.

Invite a child to come and write the number sentence on the board using the symbols – and = i.e. 10 – 4 = 6.

Repeat for other subtraction calculations.

Give each child a copy of Activity Sheet Y1 4. Ask the children to copy and complete the calculations in their books. Encourage them to use their fingers tohelp them.

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• Give each child a 0–20 number line. Tell the children that for your snack today you have a bunch of 20 grapes. Ask them to imagine 20 grapes.

Q I have 20 grapes but I eat 2. How many grapes are left?

Use a bead string, count out 20 beads, then take away 2, saying, ‘20 take away 1 is 19, take away 2 is 18’.

Model how to solve the problem using the number line. Point to 20 and say, ‘20 grapes, eat one grape leaves 19’ (as you count back one jump) ‘eat twoleaves 18’ (as you count back a second jump).

Ask children to use their number line and to count back 2 from 20.

Q Imagine I have 20 grapes but I give 5 away to my friend. How many grapes have I got left?

Encourage children to find out by using their number lines. Collect some answers then check as a class using the large number line saying, ‘20 subtract 1 is19, subtract 2 is 18, subtract 3 is 17, subtract 4 is 16 subtract 5 is 15’.

Use bead string as a concrete image: count out 20 and take away 5, saying, ‘19, 18, 17, 16, 15’ as you do so.

Q Now I have 15 grapes and I eat 3. How many do I have left?

Q Which number do I need to point to on my number line this time before I start?

Ensure the children start on 15 and then count back 3 saying 14,13,12. 12 left.

Repeat process for different calculations.

Give each child a copy of Activity sheet Y1 5 to complete. They should draw the jumps on the number lines for each question.

Q Which subtraction will need the biggest jump? Will that give the smallest answer?

Put question cards into the ‘magic’ box or bag. Invite a child to pull out a question card from the bag, for example 10 – 4 = and read the question.

Q Do we have to add or subtract? How do you know?

Q How will you work out the answer?

Encourage the children to use their whiteboards to show you the answer and any jottings that they used.

Model some different ways of solving the problem drawing on the children’s strategies which might include:I held up 10 fingers and I took away 4, leaving me with 6.I looked at the number line and counted 4 jumps back from 10.I put 10 in my head and counted back 4.I drew a number line on my board and counted back 4 jumps from 10.(Draw the jumps on the number line where these have been used.)

Invite a child to come and pull another question from the bag, for example

5 + 6 = .

Q What do we have to do? How do you know?Ask children to use their whiteboards to show you their workings and answers.Highlight different strategies:Some of you saw that this was a near double and you worked out 5 + 5 + 1 more.Some of you held up 6 fingers and counted on from 5 some counted on from 6.Some of you used a number line; you started on 5 and counted on 6.Some of you put 5 in your head and counted on 6 or counted on from 6.

Repeat this process for different questions, use numbers beyond 10 so that children have to use strategies other than counting on their fingers.

Model drawing number lines and ask the children to try that strategy too.

Put a selection of questions face down on each table. Ask children to turn over a card and copy it into their book with the answer and any jottings that theyused. Provide number lines.

• Pose question to the class. Ben went to the shop and paid 8p for an apple.

Q What coins could he use?

• Children to work with partner to find one solution and show using coins or money fan.

• Collect different suggestions.

• Record on board (try to include same answer with coins in different order).

Q Are any of these answers the same?

Q How do you know?

• Children to identify solutions with same coins in different order.

• We need to make sure we have all the answers.

• Teacher to model systematic recording of answers eg

5 + 2 + 15 + 1 + 1 + 12 + 2 + 2 + 22 + 2 + 2 + 1 + 1 etc

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Children to work in pairs on gobstopper problem - Mathematical Challenges for Able Pupils No. 2. Resource sheet Y1 6.

• Children to show answers using number fans.

• Ask children to explain their methods.

• Explain we need to be able to record what we have done.

Q What should we write?

• Talk to partner and write number sentence on whiteboards. Children to show whiteboards and choose child to write calculation on board

6 + 3 = 9

• Class to read out number sentence.

Q What is the total of 4 and 9?

• Children to show answers using number fans.

Q How can we write a number sentence to show this calculation?

• Talk to partners and show on whiteboards.

Q What do we do when we are asked for the total?

• Write calculation on board 4 + 8 = 12.

• Ask the children how they did calculation.

Q Is it easier to do 4 + 8 or 8 + 4?

Q Why? Explain reasons

• Children to pose oral questions to a partner using the words total, sum, altogether - partner to find answer and record number sentence.

What is 4 take away 2?

• Children to discuss answer with partner and hold up digit card.

• Ask children to explain their methods.

• Again we need to be able to record this. With partners children record calculation on whiteboards.

• Check whiteboards and ask child to read out calculation whilst writing number sentence on board.

4 - 2 = 2

Q What is 7 subtract 0?

• Repeat above procedure.

Q What can you tell me about taking away zero?

• Children discuss with partners. Take responses - hopefully children realise that subtracting zero leaves number unchanged. Demonstrate practically.

• Ask 9 children to stand up. Then say I want none of you to sit down.

Q How many left?

Q How can we write this number sentence?

• Children to talk to partners and write number sentence on whiteboard.

• Checks whiteboards and ask child to read out number sentence whilst writing it on the board.

Children to use digit cards. Choose 2 cards and write subtraction sum and answer either as number sentence or in pictures. Repeat using different cards

• Use ITP number facts to show 10 - 4, 10 - 6 etc then 9 - 5, 9 - 4 etc. Show corresponding number sentences.

Q If we had 7 counters how many more would we need to make 10? Show answer using number fans.

Q How could we record this calculation?

7 + = 10

• In pairs write calculation on whiteboards for partner to solve eg 6 + = 9

• Children to make sure they know answer.

Q How did you find the answers? Explain methods

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Q What number should I take away from 9 to leave 6?

Q How can we record this calculation?

9 - ∆ = 6

* 3 is the difference between 9 and 6 *

Q Can you find any other pairs of numbers with a difference of 3. Partner work.

• Give children digit cards with numbers

2, 5, 7, 9, 6

Q What is biggest difference?

Q Smallest difference?

Q Find a sum with difference of 2 etc.

• Remind children of term difference.

• Can you show me two numbers with a difference of 2? 3? 5? - using digit cards write a sum for each - whiteboard.

• Read out calculations encouraging children to use different vocabulary for subtraction.

Q I’m thinking of a number. If I take away 3 I have 7 left. What is my number? Number fans.

• Show answer using number fans.

• How could we record this calculation?

∆ - 3 = 7 - how did children solve this puzzle? What is 3?

• 3 is difference between ∆ and 7 therefore count on from 7 to find ∆ .

Q I had some grapes in a bag. I ate 7 and I only had 5 left. How many did I have to start with?

Children to work with a partner to think of problem and solution to share with class - record pictorially or in words.

Show the children the ‘Stationery Shop’, a selection of real items with price labels.

Ask questions such as:

Which item is the cheapest/costs the most?How much would you pay for a pencil?Can you find something that costs more than 5p? How much more?

Ask the children to talk in pairs and to agree questions they could ask or statements they could make using the prices. Encourage the use of a range of vocabulary. Feedback ideas.

The felt pen costs 5p. Ask the children:

Which coins could I use to pay for the felt pen?Is there more than one way to pay?

Invite children to come and show ways to pay using ‘Mega Money’. Record each solution on the whiteboard.Have we found all the ways to pay?

How could we check?

Give different groups different items from the shop to investigate all the different ways to pay. Some children could total two items and find ways to make thattotal. Keep the pencil (6p) to discuss in the plenary.

Provide pots of small coins and paper for children to record their solutions.

Show the children a ‘Stationery Shop’ with real items, priced appropriately.

Ask someone to choose 2 items to buy from the shop.

Ask:

• How much will (s)he have to pay to buy these items?

• Can you explain how you worked out the total cost?

• Which coins could (s)he use to pay the exact amount?

Children could work in pairs to find the answer and record their methods on whiteboards.

Discuss the methods used e.g. known facts, counting on, use of near doubles.

Agree that there are different ways to pay and find which uses the fewest coins.Repeat.

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Children could work in differentiated groups to find totals of 2/3 items priced as appropriate.

or

Give groups of children sets of cards made from the resource sheets, differentiated by the prices used. Place the cards face down on the table. Each pair chooses 2/3 cards and calculates the total cost of the items chosen, recording their methods. The pair with the highest total scores a point. Replace cards andrepeat.

Invite a child to choose two items to buy from a Stationery Shop with real items, priced appropriately.

Ask:

If (s)he buys these two items from the shop how can we work out how much change (s)he would get from 20p?

What would we have to work out first?

What would we have to do next?

Ask the children to work in pairs to do the first step – finding the total cost of the two items – and record their method using a number sentence on their whiteboards. Discuss the methods used and remind children that we can add the amounts in any order.

Now ask the children to do the next step in the problem – finding the change from 20p. Agree how they can find the difference between the total cost and20p.

Ask some children to share their methods and record them on the board.

Ask:

Can you show me which coins (s)he might get in her change?

Discuss the different ways that the change could be given.

Repeat.

Children could choose different items to buy and calculate the change from 20p.

Show the children a short problem – Resource Sheet Y1 7. Read through the problem together.

Remind the class that they have been solving problems about money. Today they are going to solve problems that do not involve money but they still need tothink about how to solve the problem in the same way.

• What do we need to find out?

• What is the important information?

• What operation do we need to use?

• How can we write a number sentence for that calculation?

Ask the children how they would solve the problem.Write the number sentence on the board. Remind children that we can check the total by adding in a different order.

Repeat with some of the problems on Resource sheet Y1 8 reminding children of the steps in their thinking when they are solving problems.

You could use the problem solving approach on Resource sheet Y1 9.

Children could work in groups to solve a small number of similar differentiated problems.

Show the children the problem from Resource sheet Y1 7.

Read through the problem together.Remind the class about the questions we ask ourselves to help us to solve problems.

• What do we need to find out?

• What is the important information?

• What operation do we need to use?

• How can we write a number sentence for that calculation?

Ask:

Can you tell me the number sentence we used to work out the answer to this problem?Record the number sentence on the board.

Ask:

Can anyone think of another problem that would have the same number sentence?Model how to make up a number story using contexts other than the stationery shop.Give the children time to talk in pairs about a problem that would fit this number sentence.Repeat with a selection of addition and subtraction sentences allowing time for children to work in pairs or larger groups to make up ‘number stories’.

Give groups strips of paper with individual calculations on. Ask them to make up problems/number stories to fit the calculations.

Children could draw pictures or use real items to illustrate their number story.Ask some children to be prepared to share their ideas in the plenary.

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RESOURCE SHEET Y1 1

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RESOURCE SHEET Y1 2

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RESOURCE SHEET Y1 3

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ACTIVITY SHEET Y1 4

Taking Away

10 – 1 =

10 – 2 =

= 10 – 3

= 10 – 4

6 –1 =

= 6 – 2

= 6 – 3

6 – 4 =

= 8 – 1

= 8 – 2

8 – 3 =

8 – 4 =

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ACTIVITY SHEET Y1 5

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RESOURCE SHEET Y1 6

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RESOURCE SHEET Y1 7

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RESOURCE SHEET Y1 8

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RESOURCE SHEET Y1 9

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e.3.1 describe a puzzle or problem using numbers, practical materials and diagrams

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