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# Unit Overview: Extending calculation strategies and additive reasoning

## Lessons:

30 lessons

In this lesson, we will be adjusting addends to make a calculation easier, keeping the sum the same. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 27m Video
• Transcript

### Same sum' with larger numbers

In this lesson, we will be extending the 'same sum' strategy to the addition of larger numbers. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 37m Video
• Transcript

### Same sum' with decimals

In this lesson, we will be extending the 'same sum' strategy to calculations with decimal fractions. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 31m Video
• Transcript

### Balancing equations using the 'same sum' strategy

In this lesson, we will be extending the 'same sum' rule to balance equations. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 20m Video
• Transcript

### Balancing equations using compensation

In this lesson, we will be balancing equations using the compensation property of addition and subtraction. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 16m Video
• Transcript

### Balancing equations: Does the order of addends matter?

In this lesson, we will be balancing equations and noticing that the order of the addends is not important. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 15m Video
• Transcript

In this lesson, we will notice that, if an addend is increased and the other is kept the same, the sum increases by the same amount. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 26m Video
• Transcript

In this lesson, we will notice that, if one addend is decreased and the other is kept the same, the sum decreases by the same amount Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 25m Video
• Transcript

### Solve calculations mentally by relating them to known facts

In this lesson will be solving calculations mentally by relating them to known facts. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 24m Video
• Transcript

In this lesson, we will be finding an unknown addend when the sum is changed. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 25m Video
• Transcript

### Introduction to same difference

In this lesson, we will learn about the 'same difference' strategy. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 28m Video
• Transcript

### Same difference in context

In this lesson, we will learn about contexts which focus on where the difference is kept the same. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 7m Video
• Transcript

### Use the Language of Minuend, Subtrahend, and Difference

In this lesson, we will use the some of the language of subtraction used in previous lessons- minuend, subtrahend and difference. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 17m Video
• Transcript

### Transform calculations using the same difference

In this lesson, we will transform subtraction calculations by using the "same difference" method. This method involves shifting numbers whilst preserving the answer, but making the calculation easier. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 23m Video
• Transcript

### Practice: Transforming Calculations to Make Them Easier to Solve Mentally

In this lesson, we will practise transforming calculations to make them easier to solve mentally Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 18m Video
• Transcript

### Transform a subtraction calculation to make the written algorithm easier to apply

In this lesson, we will transform a subtraction calculation between two five digit numbers to make the written algorithm easier to apply. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 25m Video
• Transcript

### Practice: 'Same Difference' in Different Contexts

In tthis lesson, we will practise the 'same difference' in different contexts. We will learn that transforming written calculations makes it easier to solve them using a written method. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 29m Video
• Transcript

### Balancing equations to find unknown values

In this lesson, we will learn to balance equations to find unknown values. We will learn how the image of a see-saw helps us think about equivalent calculations, if they are level, they are equal (equivalent) to each other. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 20m Video
• Transcript

### Explore how the difference changes when only the Minuend is changed

In this lesson, we will explore how the difference changes when only the minuend is changed. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 28m Video
• Transcript

### Apply the generalisation about how the minuend and difference change to solve problems

In this lesson, we will apply the generalisation about how the minuend and difference change to solve problems. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 19m Video
• Transcript

### Explore how the generalisation can be used as a mental calculation strategy using Known facts

In this lesson, we will explore how the generalisation can be used efficiently as a mental calculation strategy using known facts. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 27m Video
• Transcript

### Thinking flexibly

In this lesson, we will learn to think flexibly, looking for the most efficient strategies we can find for subtraction. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 29m Video
• Transcript

### Comparing Strategies

In today's lesson, we will learn to compare strategies around subtraction. We will discuss how efficient some strategies are, such as shifting to preserve the 'same difference' and make calculations easier. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 23m Video
• Transcript

### The more we subtract, the less we are left with. The less we subtract...

In this lesson, we will learn that the more we subtract, the less we are left with. The less we subtract, the more we are left with. This will be shown through the context of reduction. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 26m Video
• Transcript

### Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

In this lesson, we will apply what was learnt in the previous lesson to contexts where the minuend is kept the same, and the subtrahend increases. Different methods demonstrated will include number lines, bar models and jottings. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 11m Video
• Transcript

### Contexts where the minuend is kept the same, and the Subtrahend decreases

In this lesson, we will learn about contexts where the minuend is kept the same, and the subtrahend decreases. Different methods demonstrated within the lesson will include number lines, bar models and jottings. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 12m Video
• Transcript

### Further practice to reason about how the change in the subtrahend changes the difference

In this lesson, we will further practice to reason about how the change in the subtrahend changes the difference demonstrated through sequences. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 11m Video
• Transcript

### Explore problems in which the new difference must be found

In this lesson, we will explore problems in which the new difference must be found. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 24m Video
• Transcript

### Balance Equations Where the Compensation Property of Same Sum Cannot Efficiently be Applied

In this lesson, we will balance equations where the compensation property of same sum cannot efficiently be applied. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 21m Video
• Transcript

### Balance Equations Where the Compensation Property of Same Difference Cannot Efficiently be Applied

In this lesson, we will look at similar activities from last lesson but with subtraction in mind, specifically the following symbols: = (equals), â‰ˆ (approximately equal to) , > (greater than), < (less than). Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

• 24m Video
• Transcript