Use constant difference to balance equations and find unknowns
Lesson details
Learning outcome
I can use the same difference rule to balance equations.
Key learning points
- If I add __ to the minuend and add the same number to the subtrahend, the difference stays the same.
- If I subtract __ from the minuend and add the same number to the subtrahend, the difference stays the same.
- A number line can be used to represent the 'same difference' generalization.
Keywords
Minuend - The minuend is the number being subtracted from.
Subtrahend - A subtrahend is a number subtracted from another.
Difference - The difference is the result after subtracting one number from another.
Constant - A constant is a quantity that has a fixed value that does not change or vary, such as a number.
Unknown - An unknown is a quantity that has a set value but it is represented by a symbol or letter.
Common misconception
Lots of pupils will want to calculate the value of the expression with the known parts in order to calculate the unknown part without considering a more efficient approach.
Calculating the value of one expression is efficient with simple numbers but encourage the children to try and compare the parts instead. As the numbers get harder, calculating the expression becomes much less efficient.
Teacher tip
Ensure that the children known which parts are the minuend, subtrahend and difference before solving problems. This is particularly important in the worded problems.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Match the pairs of number complements to 100
Q2.Use a mental strategy to sum these multiples of 100
5,300 + 1,800 =
Q3.Add together these multiples of 1,000 using a mental strategy.
= 117,000 + 19,000
Q4.Complete this subtraction using a mental strategy.
367,000 − 24,000 =
Q5.How much change would I get from £20 if I spent £10.98 on a new football? £ change.
Q6.I have a ball of old plasticine that weighs 655 g and a new jumbo pack that weight 1.4 kg. What mass of plasticine do I have altogether?
Assessment exit quiz
6 Questions
Q1.Use your understanding of constant difference to work out which of the equations in the sequence is incorrect.
Q2.Use your understanding of constant difference to work out which of the equations in the sequence is incorrect.
Q3.Use constant difference to find the unknown in the equation.
65 − = 150 − 111
Q4.Use constant difference to find the unknown in the equation.
1,510 − 1,400 = − 200
Q5.Use constant difference to find the unknown in the equation.
345,000 − 236,200 = 310,000 −
Q6.At the gift shop on a residential week, Alex has £13.50 and Sofia has £9.20 to spend. They both buy a souvenir fridge magnet to take home. Sofia now has £6.21 left. How much does Alex have left?
To help you plan your 6 maths lesson on: Use constant difference to balance equations and find unknowns, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 6 maths lesson on: Use constant difference to balance equations and find unknowns, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
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