Year+2+Numeracy

MATHEMATICS Year 2 || =Using symbols=

Information ||

Objectives
• To use the ×, ÷ and = signs to record mental calculations in a number sentence • To recognise the use of a symbol to stand for an unknown number

Prior learning
To benefit from this lesson, children should: • know their 2 and 10 times tables; • be familiar with the use of multiplication and division signs.

Vocabulary
multiply, times, share, divided by, equals, number sentence

Resources
• interactive whiteboard and/or data projector linked to a laptop • Excel workbook //Using symbols// (In this Example, //Using symbols// //Excel file//) • copies of sheet 4 from the Excel workbook //Using symbols// • counters or cubes

ICT skills needed by teachers
To teach this unit, teachers need to know how to: • enter values into an Excel worksheet.

Preparation for this lesson
Before the lesson print out sufficient copies of sheet 4 from the Excel workbook //Using symbols//. Prepare the software on your computer ready for display.

Lesson extract ||

Starter
Recite the 2 and 10 times tables. Repeat each number statement twice. Ask children to whisper the statements first time, then the second time shout them. Start reciting the times table at different places. Set challenges such as: Q Can we recite the 2 times table in 30 seconds? Q Can we recite the 10 times table in 20 seconds? ===Ask children to whisper the table in time with your clapping. Vary the speed, and when you say the children are to shout the statement then whisper again. ===

Main activity
Launch the Excel workbook //Using symbols// sheet 1. Read the multiplication number sentence 3 × 2 = 6 with the class, saying ‘3 multiplied by 2 equals 6’. Q What other number must we change to make the number sentence correct if we replace the 3 with a 4? Replace the 3 with 4 and establish that the 6 must be replaced with 8. Read the sentence together: ‘4 multiplied by 2 equals 8’. Change the 4 to 7 and ask children what else must be changed. Continue asking similar questions. Each time ask the children to read aloud the new sentence. Re-enter the original number sentence 3 × 2 = 6. Q What other number must we change if we replace the 2 with a 10? Replace the 2 with 10 and establish that the 6 must be replaced with 30. Continue, this time making changes to the 3, asking children what else must be changed to make the sentence true. Each time have the children read the new sentence aloud. Open the Excel workbook //Using symbols// sheet 2, which has a multiplication number sentence where the first number is hidden by a square with the letter N in it. Explain that a number is hidden under the N. Q What is the number hidden by N? Discuss with the children their reasons for choosing the answer to the hidden number. Reveal the hidden number by shifting the box. Cover up the number again. Ask the children to close their eyes while you use the up and down arrows on the interactive spinner to increase or decrease the hidden number. Q What is N this time? Take answers and discuss reasons. Repeat hiding the first number, but keeping to the 2 and 10 times tables. Hide the number after the equals sign. Pose different questions about the possible value of N. Q Could N be an odd number? Encourage children to suggest values to test whether N can be odd. Agree that N is always even because we are multiplying by 2 or 10. Open the Excel workbook //Using symbols// sheet 3, which has the division number sentence 8 ÷ 2 = 4. Ask children to read the sentence aloud. Discuss the sentence, putting it in a context such as: 8 children sit at 2 tables; there are 4 children at each table. Ask children division-related questions such as: Q If you share 6 cakes equally between 2 plates, how many cakes are on each plate? Collect and discuss answers. Q How can we record this as a number sentence? Establish that the calculation is 6 ÷ 2 = 3, and use the interactive spinner to enter this onto the worksheet. Drag the square with the N to cover the answer, the number 3. Change the 6 to 10. Q If we had 10 cakes to share equally between the 2 plates, how many cakes are on each plate? Establish that the number hidden by N is the answer to the question. Collect and discuss suggestions. Remove the N to confirm that the answer is 5. Hide the 5 and repeat setting other problems for the children to answer using the interactive spinner to change the number sentence. Give children the Excel workbook //Using symbols// sheet 4 with number sentences and unknown numbers. They are to work out the missing numbers and fill in the column below ‘N’. Provide access to equipment (e.g. counters or cubes) where appropriate to help them carry out the calculations; for children who need support, provide sticky notes with the letter N they can use to model the hide and reveal process.

Plenary
Open sheet 4. Ask children for the answers to the missing numbers in the number sentences and enter them into the sheet. Children read the number sentences aloud, replacing N with the missing number. Launch sheet 2 or 3 to hide and reveal the numbers with the N and confirm the answers. End the lesson with some further examples where the children are to identify the hidden number. Discuss the strategies the children use and emphasise the links to the multiplication tables they recited at the start of the lesson.

Notes ||

Links to the Framework for teaching mathematics
The lesson links to units on understanding multiplication and division.

Context of this lesson
This lesson could be used in Unit 10 of the spring term from the sample medium-term plans. Children will already be familiar with the operations of multiplication and division and the corresponding signs. They may also be familiar with using a symbol such as an empty box to stand for an unknown number.

Why use ICT?
The advantages of using ICT are as follows. • The use of the interactive spinner and the opportunity to reveal numbers allows children to make and then test predictions. • ICT allows teachers to project enlarged visual images for whole-class demonstration and discussion. • The interactivity of the software is motivating and stimulating.

MATHEMATICS Year 2 || =Addition and subtraction=

Information ||

Objectives
• To know by heart: – all addition and subtraction facts for each number to at least 10 – all pairs of numbers with a total of 20 (e.g. 13 + 7, 6 + 14) • To state the subtraction corresponding to a given addition, and vice versa

Prior learning
To benefit from this lesson, children should: • recall all pairs of whole numbers with a total of 10; • understand the concept of addition, and know that subtraction can be regarded as taking away or finding a difference.

Vocabulary
add, subtract, how many more to make …?, sum, difference, total, more, less, plus, minus, altogether

Resources
• interactive whiteboard and/or data projector linked to a laptop • maths software that provides a visual model for addition and subtraction (in this Example, //Number Facts// interactive teaching program (ITP)) • wire clothes hanger, different coloured pegs, cloth to cover the pegs • mini-whiteboards and counters

ICT skills needed by teachers
To teach this unit, teachers need to know how to: • download and use the //Number Facts// ITP; • use an interactive whiteboard.

Lesson extract ||

Starter
Hold up a number of fingers, e.g. 6, and ask the children to hold up the number of fingers needed to make 10. Reinforce the number bonds by asking the children to state the number sentence, e.g. ‘six add four make ten’. Display a coat hanger with 20 pegs grouped as five pegs of one colour, then five of a different colour, then five of the first colour and finally five of the second colour. With the children, count the pegs in fives, and establish that there are four groups of five pegs. Cover 14 of the pegs on the hanger with a cloth. Q Are more than 10 pegs or fewer than 10 pegs covered up? How do you know? Establish that more than 10 pegs are hidden as two groups of five pegs are hidden, plus a few more pegs. In this case the children can only see one group of five pegs and one extra peg. Ask the children to use their whiteboards to show how many pegs are hidden. Ask children to explain their strategies. Encourage the children to think in groups of five. Draw out that four pegs need to be added to the single peg to make a group of five pegs. As two groups of five pegs and four pegs are hidden, the total number of hidden pegs must be 14. Record on the board: 6 + 14 = 20 and 14 + 6 = 20. Have the children read the number sentences aloud. Repeat by covering different numbers of pegs. Each time discuss the strategies the children use to work out the numbers of pegs that are hidden, and record and read the number sentences. Q Are there some other number sentences you could show me that we can represent using the pegs? Ask children to write these down on their whiteboards. Collect examples and record these. With the children arrange the pegs into two groups to represent the number sentence.

Main activity
Launch the //Number Facts// ITP. Set it to show 9 counters. Hide the number sentence, and ask a child to come up and tap enough counters so that 7 remain pink. Q How many counters are yellow? Q How many counters are there altogether? Ask children to write a number sentence on their whiteboards showing what they have done. Use the ITP to record the number sentence: 2 + 7 = 9. Repeat with more examples using different numbers of counters. Each time ask children to record number sentences on their whiteboards. Reset the ITP and set it to show subtraction with 9 counters. Make the container translucent. Demonstrate how to subtract 2 counters by placing them in the container. Q How many counters did we start with? How many have we taken away? How many are left? Use the ITP to record 9 – 2 = 7. Q What other number sentences could we write to show what we can see on the ITP? Add the 2 counters to the 7 counters to identify the addition corresponding to the subtraction, i.e. 7 + 2 = 9. Repeat, this time subtracting 7 counters from 9 counters, and record the statement 9 – 7 = 2 and the corresponding addition 2 + 7 = 9. Repeat with other single-digit numbers. Reset the ITP to show 16 counters. Make the container opaque and ensure that the calculation is hidden. Ask each child to write one number sentence using subtraction and the number 16. Select children to come up to the whiteboard and move counters into the container to represent their calculation while the other children have their eyes closed. Q How many counters have been put into the container? Ask the children to discuss with a partner what has happened and write on their whiteboards the number sentences that go with the calculation. Choose children to read their sentences to the class, and record the sentences on the board. Repeat the activity with different sets of counters. Give the children counters and ask them to work in groups to identify and record different number statements that involve the number 15. Q With 15 counters, what addition sentences can we write? After children have identified some addition sentences, take feedback. Stress that for every pair of numbers there are two possible addition sentences. Q Using our addition sentences, what subtraction sentences can we write? After children have identified some corresponding subtraction sentences, take feedback. Stress that for every pair of numbers there are two subtraction sentences that correspond to the two addition sentences. Record some of the calculations on the board, e.g. 5 + 10 = 15, 15 – 10 = 5, 10 + 5 = 15 and 15 – 5 = 10, and save them for use in the plenary. Encourage children to use other numbers, e.g. 14 or 17, to generate addition and subtraction sentences.

Plenary
Refer to the calculations on the board. Remind children that they used counters to help them generate these. Q What word problems can we think of that would involve the sentence 5 + 10 = 15? Prompt the children with examples such as: If we have 5 counters in a container and add another 10 counters to it, how many counters are there in the container altogether? Ask children to make up such problems with their partner for each of the four statements. Ask children a series of simple word problems involving subtraction. For example: Q There are 17 cakes in a tin. I take out 8 cakes and put them on a plate. How many cakes are left in the tin? Ask children to identify the corresponding number sentence. Use the ITP to model the subtraction and to record the related number sentence. Q What number sentence describes how many cakes there are altogether in the tin? Repeat with other word problems, each time modelling the calculation on the ITP and recording the numbers sentence.

Notes ||

Links to the Framework for teaching mathematics
The lesson links to units on addition and subtraction.

Context of this lesson
This lesson could be used in Unit 9 of the autumn term from the sample medium-term plans.

Why use ICT?
The advantages of using ICT are as follows. • The interactivity of the Interactive Teaching Program (ITP) allows the teacher to control the model in flexible ways, such as hiding and revealing counters. • ICT allows teachers to project enlarged visual images for whole-class demonstration and discussion. • The interactivity of the software is motivating and stimulating.