Adjusting addends
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)
Unit Overview: Extending calculation strategies and additive reasoning
Lessons:
30 lessons
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)
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)
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)
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)
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)
Increasing an addend
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)
Decreasing an addend
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)
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)
Find an unknown addend
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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), ≈ (approximately equal to) , > (greater than), < (less than). Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)
Units in Maths
- Number sense and exploring calculation strategies
- Place value
- Graphs
- Addition and subtraction
- Length and perimeter
- Multiplication and division
- Deriving multiplication and division facts
- Time
- Fractions
- Angles and shape
- Measures
- Securing multiplication and division
- Exploring calculation strategies and place value
- Fractions: parts and wholes
- Reasoning with 4-digit numbers
- Addition and subtraction
- Multiplication and division
- Interpreting and presenting data
- Securing multiplication facts
- Fractions
- Time
- Decimals
- Area and perimeter
- Solving measure and money problems
- 2-D Shape and Symmetry
- Position and Direction
- Reasoning with patterns and sequences
- 3D Shape
- Working with fractions
- Taking fractions further
- Reasoning with large whole numbers
- Problem solving with integer addition and subtraction
- Line graphs and timetables
- Multiplication and division
- 2-D shape, perimeter and area
- Fractions and decimals
- Angles
- Fractions, decimals and percentages
- Transformations
- Converting units of measure
- Calculating with whole numbers and decimals
- 2-D and 3-D shape
- Volume
- Problem solving with whole numbers and decimals
- Equivalent fractions
- Integers & Decimals
- Multiplication and division
- Calculation problems
- Fractions
- Missing angles and lengths
- Coordinates and shape
- Fractions
- Decimals and measures
- Percentages and statistics
- Proportion problems
- Extending calculation strategies and additive reasoning
- Doubling and halving
- Addition and subtraction within 10
- Exploring calculation strategies within 20
- Money
- Measures
- 2-D shape, perimeter and area
- Numbers to 50
- Manipulating and calculating with fractions
- Fractions
- Fractions and decimals
- Conceptualising and comparing fractions
- Numbers 50 to 100 and beyond
- Reasoning with large whole numbers
- Converting units of measure
- Numbers to 10
- Solving measure and money problems
- Addition and subtraction within 20
- Addition and subtraction (applying strategies)
- Numbers within 1000
- Place value
- Problem solving with integer addition and subtraction
- Volume
- Positive and negative numbers
- Numbers within 10
- Numbers within 15
- Addition and subtraction within 20
- Measures (1): Length and mass
- Measures (2): Capacity and volume
- Addition and subtraction of 2-digit numbers
- Fractions
- Multiplication and division
- Multiplication and division
- Axioms and arrays
- Prime factor decomposition
- Indices and standard form
- Time
- Addition and subtraction of 2-digit numbers (regrouping and adjusting)
- Area and perimeter
- Numbers and numerals
- Percentages
- Fractions
- Measures: Length
- Numbers beyond 20
- Time
- Securing multiplication facts
- Addition and subtraction within 10
- Measures: Mass
- Number sense and exploring calculation strategies
- Addition and subtraction
- Securing multiplication and division
- Position and Direction
- Pattern and Early Number
- Addition and subtraction word problems
- Fractions
- Decimals
- Multiplication and division: 3 and 4
- Multiplication and division: 2, 5 and 10
- Measures: Capacity and volume
- Addition and subtraction
- Extending calculation strategies and additive reasoning
- Deriving multiplication and division facts
- Calculating with whole numbers and decimals
- Integers & Decimals
- Multiplication and division
- Grouping and Sharing
- Surds and trigonometry
- Numbers within 6
- Numbers within 100
- Exploring calculation strategies
- Time
- Exploring calculation strategies and place value
- Multiplication and division
- Factors and multiples
- Graphs
- Graphs
- Reasoning with 4-digit numbers
- Reasoning with patterns and sequences
- Calculation problems
- Numbers within 20
- Money
- Multiplication and division
- Fractions, decimals and percentages
- Decimals and measures
- Early Mathematical Experiences
- Order of operations
- Depth of numbers within 20
- Numbers to 20
- Addition and subtraction within 20 (comparison)
- Addition and subtraction within 6
- Accuracy and estimation
- Money
- Length and perimeter
- Fractions
- Fractions
- Problem solving with whole numbers and decimals