# 6 EE 5 6 EE 6 6 EE 7 Purgatori

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```							                                   One Step Equation Test Summary

My assessment was designed for sixth grade students learning one step variable equations and
inequalities. On an original trial, it took two of my peers 15 minutes to complete the entire
assessment. After revising my exam, it took a peer of mine 30 minutes to complete. I expect my
students to take double the time, around 30 minutes to an hour to complete. Listed below are
the Common Core Standards tested in this exam:

   6.EE.5. Understand solving an equation or inequality as a process of answering a question:
which values from a specified set, if any, make the equation or inequality true? Use substitution
to determine whether a given number in a specified set makes an equation or inequality true.

   6.EE.6. Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or,
depending on the purpose at hand, any number in a specified set.

   6.EE.7. Solve real-world and mathematical problems by writing and solving equations of the
form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers

Literary Connection:

Isdell, Wendy. (1993). A Gebra Named Al: A Novel. Minneapolis: Free Spirit Publishing.

(IN TEST WITH DIRECTIONS)                                                 (JUST DIRECTIONS)
LESSON PLAN IDEAS:

There are several lessons that should be taught prior to giving this assessment to students.
Some of the lessons, although not limited to these, should include:

   Using car markers and construction paper, explain what the commutative property
means and how it works. Have students make dots with the car markers for two factors
(or addends) both vertically and horizontally. Have students discover that when the
paper is rotated (horizontal becomes vertical and vice versa) the product (or sum)
doesn’t.
   Branching off of “Danica McKellar’s Idea”, teach the middle school students that the
distributive property of multiplication is the “spreading out” of numbers and that
products can be written as the sum/difference of two numbers. Use concepts such as
area to show students that multiplying a number is the same as multiplying by the
   To teach the associative property, have students dissect the meaning of the word
“associative”. Ask students “who do you ‘associate’ with during lunch/after school?”.
Allow the student to recognize no matter the order of the grouping of pairs; the product
(or sum) does not change.
   Use ArithmeChips to teach students how to solve one step equation. Use this lesson
over a couple of days; one day teaching addition and subtraction, and another day
teaching multiplication and division. Students should build equations, trace their
findings, and explain how the question was solved. Have students actually line up and
move the chips from one side to another. This will help teach the concept: “what is done
to one side, must be done to the other”, a necessity to solving one-step equations.
   Inequalities can be better understood by using a manipulative, such as a scale. Using a
random object (to represent a variable), build and solve equations by adding other
items (make sure they are consistent since they will represent the constant) to solve the
inequality.
   Spend one or two days reading and solving algebraic story problems. Have student key
onto what words are being used in the story and their mathematical significance. For
instance, the words “of” is has meaning when multiplying, where “taking from” would
imply a subtraction problem is being studied. Teach students how to DRAW the problem
they are reading, as it is an integral part of the learning experience. Study problems that
use all four operations (addition, subtraction, multiplication, division).
Sources:

   http://www.associatedcontent.com/article/5572868/teaching_math_the_distributive_p
roperty.html?cat=4
   http://www.associatedcontent.com/article/2123099/teaching_math_the_commutative
_and_associative_pg2.html?cat=25
   http://www.amathsdictionaryforkids.com/
Assessment: Solving One-Step Equalities and Inequalities

Directions: This test will show me your skills that you have acquired to solve one
step equalities and inequalities. Take your time and answer the questions to the
best of your abilities! Remember to show all your work where necessary! You may
use a calculator on this test. Try your hardest!

Estimated Score: _____ / 35                                Actual Score: _____ / 35

1. MATCH the vocabulary word with the correct definition. Draw a line from the
vocabulary word to the corresponding definition. (1 pt each)

Equation                       A. Mathematical sentence with <,>, ≤,≥, or ≠
Like Terms                     B. Mathematical sentence with =
Constant                       C. terms with identical variables
Coefficient                    D. the number which multiplies the variable
Inequality                     E. term with no variable

2. Use your knowledge about mathematical properties to tell (3 pts each):

a) Which property is being used?

b) An algebraic expression of the property, and

c) Explain how that property works

Which property tells us that   9 x 6 = 6 x 9?

__________________________________
__________________
Which property tells us that   (2 + 7) + 4 = 2 + (7 + 4)?

___________________________________
_________________

Which property tells us that   6(5 – 3) = 6(5) – 6(3)?

____________________________________
__________________
3. For the next questions, use the cup and chips to build, draw, and explain the
equation given. Remember; use the cup as your variable and the chips as your
constants. Use complete sentences when explaining what you did. First, build
and chips using CORRECT COLOR (be consistent!); lastly, explain what you did in
Use the back of this sheet if you need more space. Take a deep breath! You can
do this!!!  (6 pts each)

A)           x+4=6
DRAW

EXPLAIN
B)        x–3   2
DRAW

EXPLAIN
Read each part of the question carefully and then respond with correct

Lindsey recently did some shopping on-line. She bought some bags of tea
and some bags of coffee. Bags of tea are \$6.00 and bags of coffee are \$9.00.
Additionally, there is a \$5.00 shipping fee for any order.
Write an expression that describes the total cost of an order. (2 pts)

If Lindsey ordered 2 tea bags and 3 bags of coffee, what was her total cost
of the order? Show all work and circle your answer! (3 pts)

Using what you know about solving one step equations, create your own
question. Be creative and think about ones that we solved during class. Be
sure there is a variable to be measured. Lastly, solve your equation. (5 pts)

```
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