lesson 3 –number -forming expressions...forming expressions fluency & precision 6 lesson 3...

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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


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


Fluency & Precision 6AnswersForming Expressions

Malachi uses cubes to write expressions for function machines.


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.


x 3x 3x + 7

Use Tia’s method to write expressions for the function machine.


x 4x 4x + 5


x 2x 2x + 3



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 Output× 9Input Output+ 3

Use two-step function machines to write expressions for the function machine.

× 6



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


x 2x 2x + 5


x 5x 5x + 4


a 7aa a + 8


x 9x 9x + 7


x 3x 3x + 3




Input OutputInput Output+ 4

Input Output÷ 3

2x

Input Output

Input Output× 2 Input Output


8x


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



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





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






Input Output

Input Output


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








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.




Input Output

Input Output


Input Output

+ 1 × 2

× 2 + 1

– 2 + 2

Answers

Answers

m 2m 2m + 1 2m + 1

m m +1 2(m + 1) 2m + 2



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.




Input Output

Input Output


Input Output

+ 1 × 2

× 2 + 1

– 2 + 2

m 2m 2m + 1 2m + 1

m m +1 2(m + 1) 2m + 2









What other pairs of functions can you think of that will do the same?

Input Output× 6




Input Output

Input Output

+ 2 × 4

× 4 + 2





Input Output× 6




Input Output

Input Output

+ 2 × 4

× 4 + 2










÷ 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.




Input Output

Input Output

+ 2 × 4

× 4 + 2





÷ 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


4m + 8Input+ 2× 4Children may use examples with numbers to show.




Input Output

Input Output

+ 2 × 4

× 4 + 2











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






Input Output

Input Output



Input Output

+ 3 × 7

× 7 + 3









7m + 21Input+ 3

× 7




Input Output

Input Output



÷ 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




7m + 21Input+ 3

× 7




Input Output

Input Output



÷ 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

lesson 3 –number -forming expressions...forming expressions fluency & precision 6 lesson 3...

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