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masterthecurriculum.co.uk
Fluency & PrecisionForming Expressions 6
Lesson 3 – Number - Forming ExpressionsNC Objective:Use simple formulaeGenerate and describe linear number sequencesExpress missing number problems algebraically
Resources needed:Differentiated SheetsTeaching Slides
Vocabulary:Algebra, two-step function, one-step function, input, output, expression
Children have now met one-step and two-step function machines with numerical inputs.In this step, children use simple algebraic inputs e.g. y.Using these inputs in a function machine leads them to forming expressions e.g. y + 4. The use of cubes to represent a variable can aid understanding.Children are introduced to conventions that we use when writing algebraic expressions. e.g. y × 4 as 4y.
Key Questions:What expressions can be formed from this function machine? What would the function machine look like for this rule/expression? How can you write x × 3 + 6 differently? Are 2a + 6 and 6 + 2a the same? Explain your answer.
Children will use the cubes to write the rules for one-step and two-step functions. They will have pictorial and functional descriptions and have to write expressions.
Children will use the cubes to write the rules for one-step and two-step functions. They will have a pictorial or functional description and have to complete more parts of the description.
Children will have either one pictorial, functional or symbolical description and have to complete the rest independently..
Reasoning & Problem Solving
Working Towards Working Within Greater Depth
masterthecurriculum.co.uk
Fluency & Precision 6Forming Expressions
Malachi uses cubes to write expressions for function machines.
Input Output× 4 Input Output+ 6
Use Malachi’s method to represent the function machines. What is the output for each machine when the input is a?
Input Output
y 5y
× 5 Input Output
y y + 5
+ 5
Tia is writing expressions for two-step function machines.
Input Output× 3 + 7
x 3x 3x + 7
Use Tia’s method to write expressions for the function machine.
Input Output× 4 + 5 Input Output× 2 + 3
masterthecurriculum.co.uk
Fluency & Precision 6AnswersForming Expressions
Malachi uses cubes to write expressions for function machines.
Input Output× 4 Input Output+ 6
Use Malachi’s method to represent the function machines. What is the output for each machine when the input is a?
Input Output
y 5y
× 5 Input Output
y y + 5
+ 5
a 4aa a + 6
Tia is writing expressions for two-step function machines.
Input Output× 3 + 7
x 3x 3x + 7
Use Tia’s method to write expressions for the function machine.
Input Output× 4 + 5
x 4x 4x + 5
Input Output× 2 + 3
x 2x 2x + 3
masterthecurriculum.co.uk
Fluency & Precision 6Forming Expressions
Input OutputInput Output
Use the cubes method to represent the function machines. What is the output for each machine when the input is a?
Input Output+ 5 Input Output× 5
Input OutputInput Output
Input Output× 9Input Output+ 3
Use two-step function machines to write expressions for the function machine.
× 6
masterthecurriculum.co.uk
Fluency & Precision 6AnswersForming Expressions
Input Output+ 2 Input Output× 6
Use the cubes method to represent the function machines. What is the output for each machine when the input is a?
a a + 2a 6a
Input Output× 2 + 5
x 2x 2x + 5
Input Output× 5 + 4
x 5x 5x + 4
Input Output× 7 Input Output+ 8
a 7aa a + 8
Input Output× 9 + 7
x 9x 9x + 7
Input Output× 3 + 3
x 3x 3x + 3
Use two-step function machines to write expressions for the function machine.
masterthecurriculum.co.uk
Fluency & Precision 6Forming Expressions
Input OutputInput Output+ 4
Input Output÷ 3
2x
Input Output
Input Output× 2 Input Output
Input OutputInput Output
8x
Use two-step function machines to write expressions for the function machine.
7a3a
4a 8aa + 8 a
Use the cubes method to represent the function machines. What is the input/output for each machine for the given input or output?
x + 2
3x + 6
masterthecurriculum.co.uk
Fluency & Precision 6AnswersForming Expressions
Input Output÷ 7 Input Output+ 4
Use the cubes method to represent the function machines. What is the input/output for each machine for the given input or output?
7a a3a 3a + 4
Input Output÷ 3 + 7
6x 2x 2x + 7
Input Output× 2 -1
x + 2 2x + 4 2x + 3
Input Output× 2 Input Output– 8
4a 8aa + 8 a
Input Output÷ 3 + 6
9x 3x 3x + 6
Input Output– 3 ÷ 4
8x + 3 8x 2x
Use two-step function machines to write expressions for the function machine.
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
What is the missing part of the function?
Input Output+ 2
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What is the missing part of the function?
Input Output
+ 1 × 2
× 2 + 1 + 2
m 2m 2m + 1 2m + 1
m m +1 2(m + 1) 2m + 2
Input Output
Input Output
+ 1 × 2
× 2 + 1
m 2m 2m + 1 2m + 1
m m +1 2(m + 1) 2m + 2
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
No, because 2m + 1 isn’t the same as 2m + 2:2m + 1Input× 2+ 12m + 2Input+ 1× 2Children may use examples with numbers to show.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What is the missing part of the function?
Input Output
+ 1 × 2
× 2 + 1
– 2 + 2
Answers
Answers
m 2m 2m + 1 2m + 1
m m +1 2(m + 1) 2m + 2
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
No, because 2m + 1 isn’t the same as 2m + 2:2m + 1Input× 2+ 12m + 2Input+ 1× 2Children may use examples with numbers to show.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What is the missing part of the function?
Input Output
+ 1 × 2
× 2 + 1
– 2 + 2
m 2m 2m + 1 2m + 1
m m +1 2(m + 1) 2m + 2
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
What is the missing part of the function?
What other pairs of functions can you think of that will do the same?
Input Output× 6
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
+ 2 × 4
× 4 + 2
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
What is the missing part of the function?
What other pairs of functions can you think of that will do the same?
Input Output× 6
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
+ 2 × 4
× 4 + 2
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
What is the missing part of the function?
What other pairs of functions can you think of that will do the same?
÷ 6Other pairs of functions that will do the same are functions that are the inverse of each other
e.g. × 5, ÷ 5.
Input Output÷ 6 × 6
Answers
Answers
No, because 4m + 2 isn’t the same as 4m + 8:4m + 2Input× 4+ 2
4m + 8Input+ 2× 4Children may use examples with numbers to show.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
+ 2 × 4
× 4 + 2
This function machine gives the same output for every input.
For example if the input is 5 then the output is 5 and so on.
What is the missing part of the function?
What other pairs of functions can you think of that will do the same?
÷ 6Other pairs of functions that will do the same are functions that are the inverse of each other
e.g. × 5, ÷ 5.
Input Output÷ 6 × 6
No, because 4m + 2 isn’t the same as 4m + 8:4m + 2Input× 4+ 2
4m + 8Input+ 2× 4Children may use examples with numbers to show.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
+ 2 × 4
× 4 + 2
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 9 then the output is 9 and so on.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What could be the missing parts of the function?
How many pairs of numbers can fit the rule of the function machine?
Input Output
+ 3 × 7
× 7 + 3
This function machine gives the same output for every input.
For example if the input is 9 then the output is 9 and so on.
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What could be the missing parts of the function?
How many pairs of numbers can fit the rule of the function machine?
Input Output
+ 3 × 7
× 7 + 3
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem SolvingForming Expressions 6
6Forming Expressions
This function machine gives the same output for every input.
For example if the input is 9 then the output is 9 and so on.
No, because 7m + 3 isn’t the same as 7m + 21:7m + 3Input× 7+ 3
7m + 21Input+ 3
× 7
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What could be the missing parts of the function?
How many pairs of numbers can fit the rule of the function machine?
÷ 6 and × 6 Other pairs of functions that will do the same are functions that are the inverse of each other
e.g. + 9, – 9.
Input Output
+ 3 × 7
× 7 + 3
× 6 ÷ 6
Answers
Answers
This function machine gives the same output for every input.
For example if the input is 9 then the output is 9 and so on.
No, because 7m + 3 isn’t the same as 7m + 21:7m + 3Input× 7+ 3
7m + 21Input+ 3
× 7
Zach inputs m into these function machines.
He says the outputs of the machines will be the same.
Do you agree? Explain your answer.
Input Output
Input Output
What could be the missing parts of the function?
How many pairs of numbers can fit the rule of the function machine?
÷ 6 and × 6 Other pairs of functions that will do the same are functions that are the inverse of each other
e.g. + 9, – 9.
Input Output
+ 3 × 7
× 7 + 3
× 6 ÷ 6