1. Add by partitioning or counting on
Calculation
Add by partitioning or counting on
Objectives
Day 1
Add pairs of 2-digit numbers by partitioning or counting on.
Day 2
Before teaching, be aware that:
On Day 1 children will need place value cards (10s and 1s), one set per pair, mini- whiteboards and pens.
On Day 2 children will need mini-whiteboards and pens. Examples for children to solve should be generated using a random number generator (alternatively or ). Please see notes with Slide 13 for tips on leading the discussion. If children would benefit from revisiting the methods use the slides from Day 1 (Slides 6, 7, 9 and 10).
Year 2

2. Add by partitioning or counting on
Calculation
Add by partitioning or counting on
Starters
Day 1
Add a single-digit number to a 2-digit number (pre-requisite skills)
Day 2
Subtract a single-digit number from a 2-digit number (pre-requisite 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 2

3. Calculation Add by partitioning or counting on Starter
Add a single-digit number to a 2-digit number
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Use Topmarks spinners at Select 2 spinners; then set values for spinner 1, TU>50. Leave spinner 2 set at 1-digit numbers. Choose children to spin both spinners then give a counter to the first 3 children to add the two numbers together. Discuss strategies used to add quickly. Spin again and repeat. Make a note of the child with the most counters at the end – you will need this when this starter is repeated in Unit 2 on Day 3.
NB If spinners animation will not run on your computer, use two sets of numeral cards for the same values.
Year 2

4. Calculation Add by partitioning or counting on Starter
Subtract a single-digit number from a 2-digit number
Pre-requisite skills – to use this starter, drag this slide to the start of Day 2
Use Topmarks spinners at Select 2 spinners and then set values for spinner 1, TU>50. Leave spinner 2 set at 1-digit numbers. Choose children to spin both spinners then give a counter to the first 3 children to subtract the second number from the first. Discuss strategies used to subtract quickly. Spin again and repeat.
NB If spinners animation will not run on your computer, use two sets of numeral cards for the same values. ?
Year 2

5. Add by partitioning or counting on
Calculation
Add by partitioning or counting on
Objectives
Day 1
Add pairs of 2-digit numbers by partitioning or counting on.
Year 2

6. Day 1: Add pairs of 2-digit numbers by partitioning or counting on.
Last term we learnt to add 2 numbers by partitioning. Work in pairs to add 32 and 24 using your place value cards.
We can record that as: = =
= 56
Let’s check…
3 0 2
2 0 4
First partition each number.
3 0
2 0 2 4
Next re-order the 10s and the 1s.
5 0 6
Add the 10s then the 1s.
Finally re-combine the numbers.
= 56
Year 2

7. Day 1: Add pairs of 2-digit numbers by partitioning or counting on.
We an also add 2 numbers by counting on, starting with the largest number.
Start at 32 and count on 2 tens. 32… 42… 52. Then 4 ones …53…54…55…56. 20 4
We can record this method on an empty number line. 32 52 56
We will get the same answer whichever method we use, so choose whichever they prefer or which you think will be the most efficient.
= 56
Year 2

8. Let’s discuss the methods we used… Draw an empty number line.
Day 1: Add pairs of 2-digit numbers by partitioning or counting on.
, , ,
Work these out on your whiteboards, using either partitioning or counting on.
Let’s discuss the methods we used…
Partitioning:
Use place value cards.
Counting on:
Draw an empty number line.
Year 2

9. Day 1: Add pairs of 2-digit numbers by partitioning or counting on.
, , ,
Let’s look at some of the calculations.
Remember you can use either method as long as you get the right answer! 20 1
Let’s check on the empty number line. 73 93 94
= 94
Year 2

10. Day 1: Add pairs of 2-digit numbers by partitioning or counting on.
Let’s check by partitioning. Watch what happens when the 1s add to more than 10.
We can record that as: = = =
= 82
4 0 7
3 0 5
First partition each number.
4 0
3 0 7 5
Next re-order the 10s and the 1s.
8 0
7 0
1 0 2
Add the 10s then the 1s.
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: Add two 2-digit numbers from number cards or customised dice, noting methods used – range of numbers used varies for each group.
Add the 70 and 10, then combine with the 2.
= 82
Year 2

11. Year 2 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: Adding two 2-digit numbers Sheet 1- complete Part A and use place value cards and number line if needed (see resources).
ARE: Adding two 2-digit numbers Sheet 1- start at the beginning and can use place value cards and number line if needed (see resources).
GD: Adding two 2-digit numbers Sheet 1- start at Part B. Encourage children to try to work the answers out in their head, then to note down their workings.
Year 2

12. Add by partitioning or counting on
Calculation
Add by partitioning or counting on
Objectives
Day 2
Add pairs of 2-digit numbers by partitioning or counting on.
Year 2

13. How would you solve this question?
Day 2: Add pairs of 2-digit numbers by partitioning or counting on.
Talk to your partner.
How would you solve this question?
Or we can use counting on.
Start with the largest number and count on the 10s then 1s.
We can draw an empty number line to help.
We could use place value cards,
partitioning each number, adding the 10s and 1s, then re-combining.
3 0 1
4 0 6
Remind children of the two methods for adding which you revised in the previous lesson.
Write the calculation on the board and ask children to think, pair, share how to solve this.
Model swapping the numbers over (as you can add in any order) and then counting on 30 and another 1 to find the answer.
Use the Top Marks spinners Select 2 spinners and then set values for spinner 1, TU<50. Do the same for spinner 2. Click in the centre of the two question marks to get the ‘add’ sign. NB If spinners animation will not run on your computer, use two sets of numeral cards for the same values.
Spin and then ask children to work with a partner to decide which method to use to add the two numbers together.
Look for examples where changing the order of the question, using number bonds etc. helps.
Remind children that when the ones add to 10 or more they have to remember to add the extra 10.
Ask two children - who chose different methods for the same question - to explain why they chose that method. 46 30 1
Year 2

14. For each example discuss which would be the best way to solve it.
Day 2: Add pairs of 2-digit numbers by partitioning or counting on.
For each example discuss which would be the best way to solve it.
Look for the most efficient way and don’t forget to use your number bonds!
Today would be a great day to use a problem-solving investigation – Diagonal Hundreds – 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: Add two 2-digit numbers from spinners, choosing appropriate methods, with support.
ARE: Add two 2-digit numbers from spinners, choosing appropriate methods OR Add two 2-digit numbers, suggesting the method to be used and devising ‘top tips’ for method selection.
GD: Add two 2-digit numbers from spinners, choosing appropriate methods, one number >50 OR Add two 2-digit numbers, suggesting the method to be used and devising ‘top tips’ for method selection.
Year 2

15. 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: Adding two 2-digit numbers Sheet 1 - use place value cards and line if needed (see resources).
ARE: More adding two 2-digit numbers Sheet 2 - use place value cards and line if needed.
GD: More adding two 2-digit numbers Sheet 2.
Challenge
Year 2

16. Add by partitioning or counting on
Calculation
Add by partitioning or counting on
Objectives
Day 1
Add pairs of 2-digit numbers by partitioning or counting on.
Day 2
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 2

17. Problem solving and reasoning questions
Look at this bar diagram.
Work out the value of the question mark.
Explain why it would be better to write this addition with the second number first.
= [__]
Choose a different method for each addition. • • •
Sam had some stickers. His sister takes 22 and he gives his friend 45.
He has none left. How many did he start with? ? 32 64
Year 2

18. Problem solving and reasoning: Answers
Look at this bar diagram.
Work out the value of the question mark.
Explain why it would be better to write this addition with the second number first.
= 77 ‘Starting with the larger number means there’s less to add on’ – this is particularly useful when the addition is done by counting on; it is less critical if the addition is done by partitioning.
Choose a different method for each addition.
• – best by partitioning since the digits are relatively large; an answer of 82 suggests child has missed the extra 10 resulting from the 1s totalling more than 10.
• – best by counting on since 10s and 1s are both small.
– counting on or noting the number bond
The key is that children are able to articulate their choice of method, neither is right or wrong.
Sam had some stickers. His sister takes 22 and he gives his friend 45. He has none left. How many did he start with? An answer of 23 suggests child has not read question carefully, a bar model should help make it clearer that this is an addition problem 96 32 64
Year 2