D.3.1 Solve Problems Involving Counting, Adding, Subtracting, Doubling or Halving in the Context of Numbers

8/7/2019 D.3.1 Solve Problems Involving Counting, Adding, Subtracting, Doubling or Halving in the Context of Numbers

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Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measuresor money, for example to pay and give change

(Objective repeated in Block A Units 2 & 3, Blocks B & D Units 1, 2 & 3 and Block E Unit 2)

Give each child a real 1p coin and a real 2p coin to hold.

Discuss what they look like.

Q What is the same about these two coins?

Q What is different?

Q Which would you rather have? Why?

Ask the children to hold up a one penny coin, then a two pence coin.

Give out further coins so that each individual has an amount up to 6p, using 1p and 2p coins.

Say to the children:- stand up if you have a total of 3 pence.- stand up if you have a total of 6 pence.

Q Who has a 2 pence coin?

Q Who has two 1 penny coins?

Q Which is worth more?

Repeat for different amounts, comparing the combinations of coins used.

Demonstrate using large coins how to count 2p coins by tapping the coin twice to keep track of how much money has been counted.

Use the large coins to demonstrate how to group 2p coins, counting these first when counting a mix of one penny and two pence coins.

Give out Activity sheet Y1 1. Ask children to find the amount of money in each purse and label it.

Set up a shop and price items using labels on Resource sheet Y1 2.

Invite volunteers to choose an item and pay for it using the exact amount. Give them real 1p and 2p coins and demonstrate to the other children howthey paid using the Mega money.

Q Which coins did Amy use?

Q Is there another way to pay?

Repeat several times.

Work with one group on the carpet and continue shopping.

Sit the children in a circle and put items from the shop in the middle.

Give each child an amount using 1p and/or 2p coins.

Ask each to find their total amount and say what they could buy.

Q How much money have you got?

Q Have you got enough to buy the?

Q Will you have any money left?

Give the other children each a copy of Activity sheet Y1 3, a collection of 1p and 2p coins.

Ask each child to find the correct coins and then write the total on the purses. Introduce a sale sign to the class for the class shop.

Q. What does this sign say?

Q. What does it mean?

Say that in our sale everything used in the class shop has 1p off.

Q. What does 1 penny off mean?

Q. Is the new price more or less than the old price?

Q.If the old price was 4 pence what is the new price?

Use a number line made of pennies (e.g. large coins on a washing line, magnetic pennies on a board, or use OHT Y1 4).

Demonstrate how to count back on this number line to find 1p less.

Using this method invite individuals to make new price labels for some of the items in the shop.

Sit the children in a circle and give each pair a price label up to 10p.

Ask children to work out the new price and hold the new sale price (i.e. 1p less than their card) in their head.

Q. I have 3p to spend, whose sale price is 3p?

Check that the child has a label saying 4p. Emphasise this to children i.e. label says 4p, therefore sale price is 3p.

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2p 2p 1p 1p

1, 2 3, 4 5 6

2p2p 2p2p 1p1p 1p1p

1, 2 3, 4 5 6


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Give the 3p to the child in exchange for 4p label.

Repeat, referring to penny number line.

When the children are confident, repeat with prices from 10p to 20p

Present Resource sheet Y1 5 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.

Q. 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.

Q. Which toy is the cheapest?

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

Q. Which toy costs more the lego or the doll?

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

Q. How much more was the lego than the doll?

Use a number line to demonstrate counting on to find how much more.

Q. If the lego costs more than the doll what could we say about the doll?

Establish that as the doll costs less than the lego 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 toys put one of the cards into a bag making sure the children can see Resource sheet Y1 5.

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 children to ask questions such as:

Q. Is the toy in the bag worth more/less than the dartboard?

Q. Is it 5p more than the ball?

Refer the children to Resource sheet Y1 5.

Tell them that they are going to buy two of the toys. Working in pairs, they can choose which toys they want and calculate 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 howthey worked 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 lego. Model the calculation on the whiteboard.

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

Establish that it is the ball and the jigsaw. Model the calculation on the whiteboard.

Ask the children:

Q. How much would it cost if we bought two dartboards?

Q. 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.

Present Resource sheet Y1 5 to the children. Read through the prices together. Tell the children that there is going to be a sale in the toy shop. Explainwhat this means to the children.

Write on the whiteboard,

2p off everything. Every toy is 2p less.

Tell the children that they are going to work out how much each toy is going to cost in the sale. Choose one of the toys eg. the lego say the children:

Q. The lego costs 8p. How much will it cost in the sale?

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When the correct answer has been given ask the children:

Q. How can we check that 6p is the correct answer?

Take responses and model the childrens method of working out using cubes and the number line.

Write the calculation on the whiteboard using and = in a number sentence.

Work through all the toys on Resource sheet Y1 5.

Draw your own set of sale items. Write price tags not less than 6p next to them. Change the labels on the whiteboard to;

5p off everything. Every item is 5p less.

Work through these new sale items as above.

At the front of the class put mega money/OHP coins in order as the children respond to questions such as:

Q. Which coin is worth the least / has the smallest value? Which coin comes next?

Chant the names of the coins with the children. Ask the children to close/cover their eyes and remove one of the coins.

Q. Which coin is missing? How did you work that out?

Present an item labelled 5p. Talk about how much it is worth; clap 5 times to match the value etc.

Give the children the pots of money. Working in pairs, ask the children to show you 5p using the coins they have. Tell the children that there is more

than one way so they can have several different answers.

Take random examples from the children and show the class using mega money/ohp coins.

Ask the children

Q. How do we know whether we have found all the different ways of making 5p?

Agree that the best way would be to work systematically starting with 1ps through to a 5p coin.1p 1p 1p 1p 1p2p 1p 1p 1p2p 2p 1p5p

Make sure the children understand that these are the only possibilities and that a combination of 1p 2p 1p 1p is the same as 2p 1p 1p 1p.

Choose another item labelled 7p and repeat the above.

Conclude by asking the children:

Q. What is the greatest number of coins we need to make 7p? What is the least? Is there one coin we can use to make 7p?

Using Resource sheet Y1 5 or items from the class shop, read through the price labels.

Working in pairs, give the children the money pots and ask the children to find the correct amount of money for each price label.

Put the mega/ohp money next to the item using the least number of coins.

Select two items. Tell the children that you would like to buy these two items. Say to the children:

What would be the first step I would have to take?

Establish that we need to work out how much they would cost altogether. Therefore we have to add the two totals together. Model the calculation using+ and = signs on the whiteboard.

Agree with the children that when they have found the total the next step is to decide which coins to use.

Q. Will we use all the coins from the beginning of the lesson?

Make sure the children understand that the coins needed are the ones, which will equal the final total rather than combining the two sets of coins. Ask thechildren

Which coin do we need to add to our mega money and money pot?

Agree that we will need a 10p coin. Model finding the total using 10p coin.

Work through several examples as a whole class. If the children are confident calculate the totals as a whole group and allow the children to find thecorrect coins using their money pots.

Set out large money coins and revise their values with the class. Order the coins on the whiteboard starting with 1p. Chant the name of the coins.

Point to a coin and ask the children:

Q. What is the name of this coin?

Q. What is the value of this coin?

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Q. How much is this coin worth?

Take a coin away and ask the children:

Q. Which coin is missing?

Q. How did you work that out?

Set up a very simple caf area couple of chairs, table, plates, etc. Have a large poster price list, Resource sheet Y1 6.

Ask questions.

Q. What is the price of a cup of coffee? (7p)

Q. Which coins would you use?

Q. Are there any other coins you could use that would still total 7p?

Using the big money show a couple of examples of coin combinations to 7p.

Show the children 5p and 1p.

Q. Which item could I buy for exactly this amount?

Work through all the items on the poster asking the questions above.

Q. Which item is the most expensive?

Q. Which item is the cheapest?

Order / list the items accordingly.

Tell the children that they are going to find out how to work out the total cost of 2 i tems and how to pay the right amount using coins.

Choose a child to be the waiter and a child to go to the caf and referring to the poster Resource sheet Y1 6 order something simple each e.g. one thing to eat, one drink Explain that you want the class to help the waiter to total the prices so that s/he can present the bill.

Working in pairs on the whiteboards children use mental addition strategies to total the bill.

Ask the children;

Q. What is the total cost of the 2 items?

Q. How did you work out the answer?

Show and draw attention to the fact that the prices can be added up in any order but the most efficient way is to start with the highest numberand count on.

Using the responses from the children model the most efficient way to find the total.

Q. How would we write this as a number sentence?

Using the responses from the children write the number sentence on the whiteboard emphasising the pence sign and the operation andequals sign.

Establish that the number sentence tells us how much the 2 items will cost the child who is buying from the caf.

The waiter then gives correct bill to the customer

Ask the children

Can you find the exact coins to match a total? What coins would the customer give to the waiter to pay the bill?

Work as a class using the mega money and find the coins to match the exact total.

Q. Can anyone show me a different way of using the coins to match the total?

Work through a couple of correct examples e.g. for 13p10p 2p 1p5p 5p 2p 1p10p 1p 1p 1p

Discuss why we wouldnt choose to use (13) 1 pence coins though it would still be correct

Establish that all the examples given are correct as they all total 13p.

Work through a second example. This time ask the children to work in pairs to write the appropriate number sentence on the pupilwhiteboards and to choose the correct amount of money from the money pots.

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Using the price list from Resource sheet Y1 6 ask the children to find a way of working out what several of one item would cost.

Q. If a glass of lemonade costs 5p, how much would 2 cost?

Q. Can you show me the right money to pay for the 2 drinks?

Discuss the ways that children found the answers and make links to their knowledge of doubling numbers

Repeat for different items in the caf.

Introduce Resource sheet Y1 7, a teddy bear and another toy that the children are familiar with and explain that it is teddys birthday and hehas invited his friend along to the caf to have a special birthday tea (extra items could be priced on a separate price list if necessary).

Outline the food and drinks/party hats etc. That are ordered e.g. 2 chocolate biscuits each, one balloon each, a glass of lemonade each etc.Limit the number of items to about 4.

Explain to the class that this is going to be a much larger bill than the previous ones and that they are all going to work together to find thetotal.

Divide the children into groups and allocate each specific items to find the cost of such as, the drinks, cakes, balloons and biscuits.

They are to work on finding the totals checking with other pairs in the group the answer is correct and recording their answer in a numbersentence using mathematical signs.

Extend the activity by asking the children to find the correct coins to match the total.

Explain to the children that in this lesson they will be investigating (finding out) how to find the cost by adding the prices of 2 items and working outthe change from 20p.

Tell the children that Teddy and his friend are going out for the day. They have each been given 20p to spend. Ask the children to find /showyou a 20p piece. Working in pairs, give the children a 20p each or give Teddy and his friend a 20p from the mega money for the children tosee.

Introduce Resource sheet Y1 8.

Teddy and his friend are going to choose 2 i tems each to buy. Suggest that Teddy wants to buy a burger and a drink.

Working in their pairs ask the children to find out how much it would cost Teddy altogether and write the number sentence on theirwhiteboards.

Establish that it would cost teddy 13p to buy the two items.

Q. Teddy has a 20p coin. Has he enough money to buy the 2 items?

Q. Has he got the right amount of money?

Q. What does the stall- holder need to give Teddy?

Discuss with children how they work out the amount of change Teddy needs.

Explain that they need to find the difference between the cost and the value of the coin.

Using a number line, model how to find the difference between 13p and 20p.

Confirm that the amount of change owing is 7p.

Repeat using different examples for Teddys friend.

Investigate finding the totals and working out the necessary change.

Show the class a short problem Resource sheet Y1 9.

Read together and ask for their ideas about how to solve it.

What do we need to find out?

What is the important information here?

What operation do we need to use? How did you find the answer? What do we do first?

How can we write a number sentence for that calculation?

After choosing one method and writing up the number sentence, ask the children if they can suggest a way to check that this answer is correct.

Take suggestions and show on the board that they can add in a different order to check the answer, count on and back.Show second problem (Resource sheet Y1 10) and explain that this time they are to try and find a different way of checking the answer.

Repeat the process of solving the problem through discussing the relevant information and choosing the appropriate operation.

Ask the children how many different ways they can think of to check the answer is correct.Put selection of items for sale at the front of the class where the children can see them.

Ask 2 children to come out and choose 1 item each.

Children then read out the cost of each item eg 6p + 3p. Teacher wants to buy both.

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Q How much will they cost?

Children to write number sentence on whiteboard to show this calculation eg 6p + 3p = 9p. Children to explain methods.

Agree the answer and write this on the board.

Show children the large magnetic coins representing 10p, 5p, 2p and 1p.

Q Which coins would I need to pay for these things?

Collect responses and show using coins the different way we could pay eg 5p + 1p + 1p + 1p + 1p or 2p + 2p + 2p + 2p + 1p etc.

Repeat procedure and extend for more able using 3 items from shop.

Activities. Children to work in pairs to buy 2/3 items from shop, record calculation and different ways to pay either in number sentences or bydrawing coins

Introduce Post Office resources to the children. Read together prices labelled on the items and ask children appropriate questions such asWhich costs more? Which item is the most expensive/ cheapest?

Tell the children that they are going to find out how to work out the total cost of 2 i tems and how to pay the right amount using coins.

Using the resources provided tell the children a story such as I need to buy a birthday card and a congratulations card. How much wil l it cost?

Working in pairs on the whiteboards children use mental addition strategies to find the total.

Ask the children

Q. What is the total cost of the 2 cards?

Q. How did you work out the answer?

Show and draw attention to the fact that the prices can be added up in any order but the most efficient way is to start with the highest number andcount on.

Using the responses from the children model the most efficient way to find the total.

Q. How would we write this as a number sentence?

Using the responses from the children write the number sentence on the whiteboard emphasising the pence sign and the operation and equalssign.

Establish that the number sentence tells us how much the 2 cards will cost.

The Post Office master then gives correct bill to the customerAsk the children

Q. Can you find the exact coins to match a total? What coins could the customer use to pay the bill?

Work as a class using the mega money and find the coins to match the exact total.

Q. Can anyone show me a different way of using the coins to match the total?

Work through a couple of correct examples e.g. for 12p10p 2p5p 5p 2p10p 1p 1p

Discuss why we wouldnt choose to use (12) 1 pence coins though it would still be correctEstablish that all the examples given are correct as they all total 12p.

Work through a second example.

This time ask the children to work in pairs to write the appropriate number sentence on the pupil whiteboards and to choose the correct amount ofmoney from the money pots.

Using Post Office Resources ask the children to find a way of working out what several of one item would cost.

Q. If one birthday card costs 9p, how much would 2 birthday cards cost?

Discuss the ways that children found the answers and make links to their knowledge of doubling numbers

Q. Can you show me the exact coins to pay for the 2 cards?

Accept several examples and then using a new example e.g. 2 stamps costing 7p each tell the children that they have to:

Find out the total cost of 2 stamps.

Show the exact amount using the least number of coins.

Allow the children time to solve this problem in pairs.

Establish that the least number of coins to show 14p would be 3 coins.

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Show the children a selection of items from the post office. Put a price card by each item to show the prices a selection of prices up to 10p.

Tell the children that today they are going to choose which two items they want to buy from the post office. They are going to work out the total costfor the two items and write the appropriate number sentence.

Working in pairs, allow a few minutes for the children to make their selection and write the number sentence onto their whiteboards.

Take responses and demonstrate a few examples on the board. Ask the children;

Now that you have found the total cost can you work out what change you would have from 20p?

Clarify how they would work this out and allow the children time to work in their pairs finding the correct change.

Take responses and demonstrate a few examples on the board. Ask the children;

Now that you know what change you would have from 20p, can you show me that amount using the coins?

When the children have been given the opportunity to select the correct coins for their change, choose an example where children have the sameamount of change but have used different coins.If this does not occur, use your own example.

Pair A have 5p change and they have chosen a 5p coin and Pair B have 5p change but they have used a 2p, 2p and 1p. Are both these answerscorrect?Are there any other possible combinations of coins?

Working with their own examples, ask the children to think of as many different combinations as possible. Record their answers using coins orwriting them onto their whiteboards.

Put the total cost of two items onto the whiteboard e.g. 15p. Tell the children that this was how much it cost when you went shopping at the postoffice.

Which two items did I buy?

Allow the children time to work out the answer in their pairs.

How do you know that is the correct answer?

What change would I have been given from 20p?

Show the class a short problem Resource sheet Y1 11.

Read together and ask for their ideas about how to solve it.


What is the important information here?

What operation do we need to use?

How did you find the answer? What did you do first?


After choosing one method and writing up the number sentence, ask the children if they can suggest a way to check that this answer is correct.

Take suggestions and show on the board that they can add in a different order to check the answer.Show second problem (Resource sheet Y1 12)

Repeat the process of solving the problem through discussing the relevant information and choosing the appropriate operation.

Ask the children how many different ways they can think of to check that the answer is correct.

Discuss the suggestions and try them out, showing on the board. Make links with the fact that subtraction and counting on are linked.

Present Resource sheet Y1 13 to the children. Repeat the process of solving the problem through discussing the relevant information and choosingthe appropriate operation.

Allow the children time to investigate the answers independently. Encourage the children to record their working and solutions to the problem.

Show the children the Stationery Shop Resource sheet (Y1 14) or set out a selection of similar 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 arange of vocabulary. Feedback ideas.

The felt pen costs 5p. Ask the children:

Which coins could I use to pay for the felt pen?

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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 tomake that total. 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 the Stationery Shop resources. Resource sheet Y1 14.

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.

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 apoint. Replace cards and repeat.

Invite a child to choose two items to buy from the Stationery Shop. Resource sheet Y1 14.

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 totalcost and 20p.

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 15. Read through the problem together.


What is the important information?



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 16 reminding children of the steps in their thinking when they are solving problems.

You could use the problem solving approach on Resource sheet Y1 17.

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

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Show the children the problem from Resource sheet Y1 15.Read through the problem together.Remind the class about the questions we ask ourselves to help us to solve problems.


What is the important information?



Ask:Can you tell me the number sentence we use 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 numberstories.

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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ACTIVITY SHEET Y1 1

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RESOURCE SHEET Y1 2

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ACTIVITY SHEET Y1 3

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OHT Y1 4

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RESOURCE 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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RESOURCE SHEET Y1 10

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Liam wants to buy

How much money does he need?

What change will we have from 20p?

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3p

and

11p


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Documents

D.3.1 Solve Problems Involving Counting, Adding, Subtracting, Doubling or Halving in the Context of Numbers