Rich Task: Expressions and substitution (Topic 2.1, Mathematics and Statistics Year 7)

Oxford Mathematics and Statistics 7 for Aotearoa New Zealand Rich task 2.1

Expressions and substitution 1. Create at least two different expressions that simplify to 6 a+ 4 , including an easy version and a trickier version. Your expression:   

must include at least 4 terms must include at least one subtraction can include numbers and variables

2. Decide if these are always, sometimes, or never true and explain your reasoning why. a. 4 x+3 x=7 x b. 6 y− y=5 c. 2 x+3+ x=3 x+3 d. 5 a+2 b=7 ab

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Teacher notes Curriculum links

Equations and relationships

KNOWLEDGE

PRACTICES

A variable can be used to represent: an unknown number, often in formulae (e.g. s in s2) o a quantity that can vary or change (e.g. y=3 x +4 ; A=bh) o a specific unknown value to be solved (e.g. 3 a=18).

Algebra has its own specialised notation to express relationships and operations concisely, including: o 3 b in place of b+ b+b , 3 ×b , and b ×3 o b in place of 1 b o ab in place of a × b or b × a (in alphabetical order) o a 2 in place of a × a, a 3 in place

Simplifying expressions involving any of the four operations by collecting like terms (e.g.

3 a+ a+a=5 a, 3 b−2 b=b ) Using substitution to find the value of an expression or formula (e.g. calculating w +12 given w=4 )

of a × a ×a

a 1 in place of a ÷ b and a × b b o a in place of a 1. o

Possible answers 



Question 1 There are many possible answers for 6 a+ 4 , including: o 3 a+2 a+ a+6−2=(3 a+2 a+ a)+(6−2) o 10 a−4 a+3−1+2=(10 a−4 a)+(3−1+2) o 2 a+2+ 4 a+5−3=(2 a+ 4 a)+(2+5−3) o 8 a−2 a+7−3=(8 a−2 a)+(7−3) o 12 a−3 a−3 a+ 10−6=(12 a−3 a−3 a)+(10−6) Question 2 o 4 x+3 x=7 x : Always true Why: Both terms are like terms (they both have x ).

You can add the coefficients: 4 +3=7, so 4 x+3 x=7 x . o 6 y− y=5: Sometimes true Why: When you simplify the left side: 6 y− y=5 y , so the equation becomes: 5 y=5 . This is only true when y=1 . o 2 x+3+ x=3 x+3 Always true Why: Combine like terms on the left: 2 x+ x=3 x , so 2 x+3+ x=3 x+3 Both sides are identical after simplifying o 5 a+2 b=7 ab : Sometimes true Why: 5a and 2b are not like terms (different variables), so you cannot add them together.

Also, 7ab means multiplication, not addition.

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However, the equation is true if b= and b .

5a (e.g. a=b=0) so it can be true for specific values of a 7 a+2

What to notice and look for Do the students;  Combine ‘a’ terms to make6 a  Combine constants to make + 4  Keep terms separate until simplified

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