Equations & Expressions Small Tasks
Task I.
Hearts and Stars!
http://www.nctm.org/store/Products/Implementing-the-Common-Core-State-Standardsthrough-Mathematical-Problem-Solving,-Grades-6-8
If  +  +  +  +  = 18
And  +  = 8
What is the value of one ? What is the value of one?
Task II.
Correct or Incorrect?
http://www.nctm.org/store/Products/Implementing-the-Common-Core-State-Standardsthrough-Mathematical-Problem-Solving,-Grades-6-8/
For each of the following, a student evaluated the given expression. Your job is to determine
whether the student is correct or not. If you think the student is wrong, explain the mistake and
provide the correct answer.
a. Fiona says that 12 ÷ 4 ∙ 3 = 1
b. Malia says that 10 − 2(5 + 11) = −22
c. Kevin says that 3 − 2 + 1 − 4 = −2
d. Tyler says that 52 + 12 = 36
e. Carlos says that
10+1+4
5
=7
f. Jennifer says that 2𝑥 + 3 = 5𝑥
g. Lillian says that 3(𝑥 + 2𝑦) = 3𝑥 + 2𝑦
Task III.
What’s the Number?
In each equation below, x can be replaced with a number that makes the equation true. Find
such a number.
https://www.illustrativemathematics.org/content-standards/6/EE/A/1/tasks/2226
a. 64 = 𝑥 2
f. 2 ∙ 25 = 2𝑥
b. 64 = 𝑥 3
g. 2𝑥 = 24
c. 2𝑥 = 32
h. 43 = 8𝑥
2 3
d. 𝑥 = (5)
e.
16
9
=𝑥
2
NCDPI Secondary Math
i.
𝑥 2 = 25
j.
(𝑥 + 1)2 = 25
MS EE Coherence PD
Equations & Expressions Small Tasks
Task IV.
Quotient Rule
https://www.illustrativemathematics.org/content-standards/8/EE/A/1/tasks/1438
In this problem 𝑐 represents a positive number.
The quotient rule for exponents says that if 𝑚 and 𝑛 are positive integers with 𝑚 > 𝑛, then
𝑐𝑚
𝑐𝑛
= 𝑐 𝑚−𝑛 .
After explaining to yourself why this is true, complete the following exploration of the quotient rule
when 𝑚 ≤ 𝑛:
a. What expression does the quotient rule provide for
𝑐𝑚
𝑐𝑚
𝑐𝑛
when 𝑚 = 𝑛?
b. If 𝑚 = 𝑛, simplify 𝑐 𝑛 without using the quotient rule.
c. What do parts (a) and (b) above suggest is a good definition for 𝑐 0 ?
𝑐0
d. What expression does the quotient rule provide for 𝑐 𝑛?
𝑐0
e. What expression do we get for 𝑐 𝑛 if we use the value for 𝑐 0 found in part (c)?
f. Using parts (d) and (e), propose a definition for the expression 𝑐 −𝑛 .
Task V.
Delivery Trucks
A company uses two different-sized trucks to deliver sand. The first truck can transport cubic yards,
and the second cubic yards. The first truck makes trips to a job site, while the second makes trips.
What quantities do the following expressions represent in terms of the problem's context?
https://www.illustrativemathematics.org/content-standards/HSA/SSE/A/1/tasks/531
a. 𝑆 + 𝑇
b. 𝑥 + 𝑦
c. 𝑥𝑆 + 𝑦𝑇
d.
Task VI.
𝑥𝑆+𝑦𝑇
𝑆+𝑇
Moving Parentheses!
Evaluate the following numerical expressions.
https://www.illustrativemathematics.org/content-standards/6/EE/A/tasks/1136
a. 2(5 + 3)(2) + 4)
b. 2((5 + 3)(2 + 4))
c. 2(5 + 3(2 + 4))
Can the parentheses in any of these expressions be removed without changing the value of the
expression?
NCDPI Secondary Math
MS EE Coherence PD
Equations & Expressions Small Tasks
Task VII.
What’s the Difference?
Write an expression for the sequence of operations.
https://www.illustrativemathematics.org/content-standards/7/EE/A/1/tasks/541
a. Add 3 to 𝑥, subtract the result from 1, then double what you have.
b. Add 3 to 𝑥, double what you have, then subtract 1 from the result.
Task VIII.
Tell the Truth!
Decide whether each equation is true or false, and explain how you know.
https://www.illustrativemathematics.org/content-standards/6/EE/A/1/tasks/2225
a. 24 = 2 ∙ 4
b. 3 + 3 + 3 + 3 + 3 = 35
c. 53 = 5 ∙ 5 ∙ 5
d. 23 = 32
e. 161 = 82
f. (1 + 3)2 = 12 + 32
g. 2 ∙ 2 ∙ 2 ∙ 3 ∙ 3 ∙ 3 = 63
Task IX.
Amusement Park Tickets
Malia is at an amusement park. She bought 14 tickets, and each ride requires 2 tickets.
https://www.illustrativemathematics.org/content-standards/7/EE/A/2/tasks/1450
a. Write an expression that gives the number of tickets Malia has left in terms of 𝑥, the number
of rides she has already gone on. Find at least one other expression that is equivalent to it.
b. 14 − 2𝑥 represents the number of tickets Malia has left after she has gone on 𝑥 rides. How
can each of the following numbers and expressions be interpreted in terms of tickets and
rides?
14
−2
2𝑥
c. 2(7 − 𝑥)
also represents the number of tickets Malia has left after she has gone on 𝑥
rides.
How can each of the following numbers and expressions be interpreted in terms of tickets
and rides?
7
(7 − 𝑥)
2
Task X.
Blueprint
Maggie is working from a blueprint in which 3 inches represents 14 feet. Write an equation that
represents the relationship between the actual lengths (a), in feet, and the blueprint lengths (b),
in inches?
NCDPI Secondary Math
MS EE Coherence PD