Multiplication and Division Counting in equal steps Sequences Objectives Day 1 Count in 50s and 100s. Day 2 Count in 4s and 8s. Day 3 Work out the rule for a sequence. Before teaching, be aware that: On Day 1 children will need mini-whiteboards and pens. You will need Counting stick On Day 2 children will need mini-whiteboards and pens. You will need Internet access On Day 3 children will need mini-whiteboards and pens. Year 3

Multiplication and Division Counting in equal steps Sequences Starters Day 1 Count in 100s (pre-requisite skills) Day 2 Odd and even numbers (simmering skills) Day 3 Count back in 3s (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 3

Multiplication and Division Counting in equal steps Sequences Starter Count in 100s Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Use http://www.ictgames.com/mobilePage/flipCounter/index.html to count in steps of 100 from 31 to 1031 and back again. Repeat, this time starting at 68.   Year 3

Multiplication and Division Counting in equal steps Sequences Starter Odd and even numbers Simmering skills – to use this starter, drag this slide to the start of Day 2 Use a random number generator such as at https://www.google.com/search?q=random+number to generate numbers between 1 and 100. Children call out odd or even accordingly. As children become more confident, extend to generate numbers between 100 and 1000.   Year 3

Multiplication and Division Counting in equal steps Sequences Starter Counting back in 3s Simmering skills – to use this starter, drag this slide to the start of Day 3 Children work in groups. The first person says 55, the next person subtracts 3 and says the new number (52), the next says 49 and so on. The first group to say ‘1’ wins! Repeat from different starting points that are 1 more than multiples of 3, e.g. 49, 34, 61 etc.   Year 3

Multiplication and Division Counting in equal steps Sequences Objectives Day 1 Count in 50s and 100s. Year 3

Day 1: Count in 50s and 100s. Let’s count in 10s from 0 to 100 on the counting stick. 50 Either use a counting stick or the slides. Which number is halfway between 0 and 100? Year 3

Now let’s count in 100s from 0 to 1000. Day 1: Count in 50s and 100s. Now let’s count in 100s from 0 to 1000. 100 200 300 400 500 600 700 800 900 1000 Year 3

How about counting on from 78 in 100s and back again? Day 1: Count in 50s and 100s. How about counting on from 78 in 100s and back again? 78 178 278 378 478 578 678 778 878 978 Year 3

Now count on in steps of 100 from 341. Day 1: Count in 50s and 100s. Write down the next three numbers in the sequence. Now count on in steps of 100 from 341. 341 441 541 641 Year 3

Day 1: Count in 50s and 100s. Write down the next three numbers in the sequence. Now count on in steps of 100 from 197. 197 297 397 497 Year 3

Day 1: Count in 50s and 100s. Write the next three numbers in the sequence. Finally, count on in steps of 100 from 614. 614 714 814 914 Year 3

Now let’s count in steps of 50 to 1000 and back. Day 1: Count in 50s and 100s. Now let’s count in steps of 50 to 1000 and back. 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 Year 3

Write the next three numbers... Day 1: Count in 50s and 100s. Look at this sequence. 4, 54, 104, 154 4 + 50 = 54 Challenge 54 + 50 = 104 Write the next three numbers... 104 + 50 = 154 Year 3

Did you follow the pattern? Day 1: Count in 50s and 100s. Did you follow the pattern? 4, 54, 104, 154, 204, 254, 304 Year 3

Write the next three numbers. Day 1: Count in 50s and 100s. Now try this one. 23, 73, 123, 173 23 + 50 = 73 Challenge 73 + 50 = 123 Write the next three numbers. 123 + 50 = 173 Year 3

Did you follow the pattern? Day 1: Count in 50s and 100s. Did you follow the pattern? 23, 73, 123, 173, 223, 273, 323 Today would be a great day to use a problem-solving investigation – Dog Chews – 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/ARE/GD: Play ‘Ping Pong’, alternating between counting in 100s and 50s to 1000. WT/ARE/GD: Play ‘Jump 50, Jump 100’, counting on a given number of 100s or 50s. Year 3

Challenge 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: Count in steps of 100 Sheet 1 ARE/GD: Count in steps of 100 and 50 Sheet 2 Year 3

Multiplication and Division Counting in equal steps Sequences Objectives Day 2 Count in 4s and 8s. Year 3

What did you notice about all the numbers we said? Day 2: Count in 4s and 8s. We’re going to count round the class in steps of 4 from 4 to at least 100! What did you notice about all the numbers we said? They were all even! Slow down a little when you get past 48. Year 3

Join in with the counting song… Day 2: Count in 4s and 8s. Join in with the counting song… Write the numbers in the count to 96, one underneath each other. What did you notice about all of these numbers? They are even too! Play the Counting By Eights Song at http://www.youtube.com/watch?v=3SwaOvWD-PY (starting at 1:30). Year 3

To find the digital root of 32 we add 3 and 2 to give 5. Day 2: Count in 4s and 8s. To find the digital root of 32 we add 3 and 2 to give 5. To find the digital root of 96 we add 9 and 6 to give 15, then 1 and 5 to give 6. Year 3

Do you notice any patterns? Can you explain why they might occur? Day 2: Count in 4s and 8s. Have a go at finding digital roots with the sequence of numbers in the 4 times table. Challenge Do you notice any patterns? Can you explain why they might occur? 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/ARE/GD: Find the digital roots of numbers in the 4 and 8 times table and beyond. WT/ARE/GD: Play the compound leaves game, counting in 4s and 8s. Year 3

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: Missing numbers Sheet 1 Challenge Year 3

Multiplication and Division Counting in equal steps Sequences Objectives Day 3 Work out the rule for a sequence. Year 3

Can you try to describe the rule for this sequence? Day 3: Work out the rule for a sequence. Can you try to describe the rule for this sequence? 28, 24, 20 Write it on your whiteboard as well as the next three numbers in the sequence. Year 3

28, 24, 20, 16, 12, 8 Day 3: Work out the rule for a sequence. The rule is subtract 4 each time. Sequences can decrease as well as increase. 28, 24, 20, 16, 12, 8 Year 3

Now look at this sequence. Can you describe the rule? Day 3: Work out the rule for a sequence. Now look at this sequence. Can you describe the rule? Write it on your whiteboard as well as the next three numbers in the sequence. 2, 6, 10 Year 3

2, 6, 10, 14, 18, 22 Day 3: Work out the rule for a sequence. The rule is + 4 each time. 2, 6, 10, 14, 18, 22 Year 3

Challenge Day 3: Work out the rule for a sequence. Work with a partner. Create and continue increasing and decreasing sequences for your partner to write the rule and the next 3 numbers. Come back together and share some of the sequences. Year 3

Look at this sequence. Can you describe the rule? Day 3: Work out the rule for a sequence. Look at this sequence. Can you describe the rule? Write it on your whiteboard as well as the next three numbers in the sequence. 2, 4, 8 Year 3

The rule is to double each time. Day 3: Work out the rule for a sequence. The rule is to double each time. 2, 4, 8 , 16, 32, 64 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/ARE/GD: Play sequences card game, challenging a partner to spot the rule of a sequence and write the next three numbers. WT/ARE/GD: Play sequences game, identifying the rule for a given sequence of numbers. Year 3

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: What’s the pattern? Sheet 1 ARE/GD: What’s the pattern? Sheet 2 Challenge Year 3

Multiplication and Division Counting in equal steps Sequences Well Done! You’ve completed this unit. Objectives Day 1 Count in 50s and 100s. Day 2 Count in 4s and 8s. Day 3 Work out the rule for a sequence. 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 3

Problem solving and reasoning questions Write the next four numbers in these sequences: • 4, 8, 12, … • 13, 63, 113, … • 8, 16, 24, … • 100, 96, 92, … • 341, 441, 541, … • 601, 551, 501, … Create a sequence of ten numbers where you count on in 8s from an odd number. Harry says, ‘If I count in 4s, starting at 3, I won’t say 30, but I will say 303.’ Do you agree? Explain your ideas. Year 3

Problem solving and reasoning questions Write the next four numbers in these sequences: • 4, 8, 12, 16, 20, 24, 28. (increasing in 4s). • 13, 63, 113, 163, 213, 263, 313. (increasing in 50s) • 8, 16, 24, 32, 40, 48, 56. (increasing in 8s) • 100, 96, 92, 88, 84, 80, 76. (decreasing in 4s) • 341, 441, 541, 641, 741, 841, 941. (increasing in 100s). • 601, 551, 501, 451, 401, 351, 301. (decreasing in 50s). Create a sequence of ten numbers where you count on in 8s from an odd number. e.g. 7, 15, 23, 31, 39, 47, 55, 63, 71, 79. Harry says, ‘If I count in 4s, starting at 3, I won’t say 30, but I will say 303.’ Do you agree? Explain your ideas. Harry is correct. Counting on in 4s: 3, 7, 11, 15, 19, 23, 27, 31… so he doesn’t say 30. Since 100 is a multiple of 4 he will say 103, 203, 303… Children may count on to 103 and then realise that the sequence of 2-digit endings will repeat. Year 3