Place Value Negative numbers Count through zero Objectives Day 1 Compare and order negative numbers. Day 2 Count back in steps through zero. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. You may wish to use the ITP Number line (see resources). On Day 2 children will need mini-whiteboards and pens. Year 5

Place Value Negative numbers Count through zero Starters Day 1 Count back through zero (pre-requisite skills) Day 2 Count on and back in steps of 25 (simmering skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 5

Count back through zero Place Value Negative numbers Count through zero Starter Count back through zero Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Hold a counting stick vertically. Count back in 1s from 5 at the top: 5, 4, 3, 2, 1, 0. What comes next? Continue, negative one, negative two … negative five. Remind children that numbers less than 0 are called negative numbers, and numbers more than 0 are called positive numbers. Write 0, –2 and –4 on sticky notes. Point to the top. If this is 5 and we count down in 1s, where should we stick 0? –2? –4? Turn the counting stick so that it is horizontal. Point to the left, as children see it. This is –5. Count from –5 to 5, speeding up as you pass 0, then count back again. Ask 3 children to place the sticky notes on the stick. Year 5

Count on and back in steps of 25 Place Value Negative numbers Count through zero Starter Count on and back in steps of 25 Simmering skills – to use this starter, drag this slide to the start of Day 2 Use the counting stick to support counting in steps of 25 from 0 to 250 and back again. Repeat, this time from 3 to 253, then 13 to 263 and back again. Count slowly to begin with. Year 5

Place Value Negative numbers Count through zero Objectives Day 1 Compare and order negative numbers. Year 5

When might we use negative numbers? Day 1: Compare and order negative numbers. When might we use negative numbers? We often say ‘minus’ rather than ‘negative’, particularly with temperatures below 0°C. temperature, depth below sea level, overdrafts… What numbers are marked? How do you know? -–2 > –8 Which number is greater? -8 -2 Take feedback. Agree that –3, –4, –5, –6 and –7 are all in between. Write a number between –2 and –8 on your whiteboards. Year 5

Day 1: Compare and order negative numbers. What numbers are marked? How do you know? -3 > –4 Which number is greater? -4 3 Write a number between –4 and 3 on your whiteboards. Year 5

Write a number between –15 and 15 on your whiteboard. Day 1: Compare and order negative numbers. Write a number between –15 and 15 on your whiteboard. Now, let’s use these numbers to make a number line from –15 to +15… Call out the names of the first five children from the register. Call out the names of the next five children from the register. Stand up at the front of the class with your numbers in the correct order: smallest on the left (as the rest of the class see you), largest on the right. Place yourselves in the correct place in the line. What will you do if some of you have the same number? Is there a new smallest/ largest number? Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Practise ordering number cards –10 to 10. ARE/GD: Order sets of three –15 to 15 number cards using < and >. Play a team game. Continue until all children are in the line! Are there any numbers missing from our number line? Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE/GD: Order positive and negative numbers. WT: Children have -10 to 10 number lines to help (see resources). All children attempt Challenge. Challenge Year 5

Place Value Negative numbers Count through zero Objectives Day 2 Count back in steps through zero. Year 5

We are going to count on in 2s. Where do you think we will get to? Day 2: Count back in steps through zero. –10 –8 –6 –4 –2 2 4 6 8 10 We are going to count on in 2s. Where do you think we will get to? Count on in 2s, speeding up as you pass 0, then count back again. Now let’s count back again… Year 5

We are going to count on in 5s. Where do you think we will get to? Day 2: Count back in steps through zero. –40 –35 –30 –25 –20 –15 –10 –5 5 10 We are going to count on in 5s. Where do you think we will get to? Count on in 5s, speeding up as you pass 0, then count back again. Now let’s count back again… Year 5

We are going to count on in 10s. Where do you think we will get to? Day 2: Count back in steps through zero. –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 We are going to count on in 10s. Where do you think we will get to? Count on in 10s, then count back again. And back again… Year 5

We are going to count on in 25s. Where do you think we will get to? Day 2: Count back in steps through zero. –200 –175 –150 –125 –100 –75 –50 –25 25 50 We are going to count on in 25s. Where do you think we will get to? Count on in 25s, speeding up as you pass 0, then count back again. Now let’s count back again… Year 5

Day 2: Count back in steps through zero. This time we are going to count back from 20 in 3s. –19 –16 –13 –7 –4 –1 2 8 11 14 17 We need to take particular care when counting back and crossing zero. Year 5

This time we are going to count back from 20 in 6s. Day 2: Count back in steps through zero. This time we are going to count back from 20 in 6s. –16 –4 2 8 14 Year 5

This time we are going to count back from 20 in 2.5s. Day 2: Count back in steps through zero. This time we are going to count back from 20 in 2.5s. –17.5 –12.5 –7.5 –2.5 2.5 7.5 12.5 17.5 Year 5

Day 2: Count back in steps through zero. If we have 3 subtract 4, we would normally say we can’t do it, but we can if we use negative numbers. What is 3 subtract 4? –1 3 Make up your own subtractions with a negative answer. Where in ‘real life’ are these sorts of subtractions possible? Discuss situations in ‘real life’ where these sorts of subtractions are possible, e.g. falls in temperature, descending below sea level, or being overdrawn at the bank. Today would be a great day to use a problem-solving investigation – First Connect Three – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Play a game to practise counting back through zero to -20 and beyond. ARE/GD: Repeatedly subtract from the first number in a given pair to exactly reach the second. Year 5

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT/ARE:/GD: Count in steps through zero. WT: Children draw hops on -20 to 20 number lines to help (see resources). GD: Children complete the Challenges. Challenge Year 5

Well Done! You’ve completed this unit. Place Value Negative numbers Count through zero Well Done! You’ve completed this unit. Objectives Day 1 Compare and order negative numbers. Day 2 Count back in steps through zero. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 5

Problem solving and reasoning questions Sketch a line -20 to +20. Mark 0. Teacher marks a mystery number (e.g. -8). What number have I marked? Children ask question to guess. Repeat. How many (whole) numbers are there between -11 and +11 which have just one digit? Count in steps of -5. Start at +3. How many steps to get to –42? Order these temperatures, starting with the lowest: 12°C -6°C -11°C 0°C 27°C Year 5

Problem solving and reasoning: Answers Sketch a line -20 to +20. Mark 0. Teacher marks a mystery number (e.g. -8). What number have I marked? Children ask question to guess. Repeat. Some children may confuse phrases like ‘is it more/less than’ when applied to negative numbers How many (whole) numbers are there between -11 and +11 which have just one digit? 12 steps: -27, -23, -19, -15, -11, -7, -3, 1, 5, 9, 13, 17, 21 Count in steps of -5. Start at +3. How many steps to get to –42? 9 steps: An answer of 10 suggests that +3 (the start number) has been counted as a step. Some may be confused with the initial step which crosses zero. Children should note the pattern in the 1s digits of the negative numbers.   +3, -2, -7, -12, -17, -22, -27, -32, -37, -42 Order these temperatures, starting with the lowest: 12°C -6°C -11°C 0°C 27°C -11°C -6°C 0°C 12°C 27°C Watch for children who order the numbers ignoring the negative number signs, i.e. 0, 6, 11, 12, 27 or who reverse the order of the two negative numbers putting -6°C before -11°C. Year 5