CORE Assessment Module
Module Overview
Content Area
Title
Grade Level
Problem Type
Standards for
Mathematical
Practice
Mathematics
Least and Greatest
Grade 7
Performance Task
Mathematical Practice 1 (MP1): Make sense of problems and persevere in solving them.
Mathematically proficient students:
 Explain to themselves the meaning of a problem and look for entry points to
its solution.
 Analyze givens, constraints, relationships, and goals.
 Make conjectures about the form and meaning of the solution and plan a
solution pathway rather than simply jumping into a solution.
 Consider analogous problems, and try special cases and simpler forms of the
original problem in order to gain insight into its solutions.
 Monitor and evaluate their progress and change course if necessary.
 Transform algebraic expressions or change the viewing window on their
graphing calculator to get information.
 Explain correspondences between equations, verbal descriptions, tables, and
graphs.
 Draw diagrams of important features and relationships, graph data, and
search for regularity or trends.
 Use concrete objects or pictures to help conceptualize and solve a problem.
 Check their answers to problems using a different method.
 Ask themselves, “Does this make sense?”
Understand the approaches of others to solving complex problems and identify
correspondences between approaches.
7.NS.1 Apply and extend previous understandings of addition and subtraction to
add and subtract rational numbers.
Common Core
State
Standards
Claim 1: Concepts and Procedures—Students can explain and apply mathematical
SBAC
concepts and interpret and carry out mathematical procedures with
Assessment
precision and fluency.
Claims
In the first part, students will add and multiply rational numbers to create the least
Task
and greatest numbers from a given set of numbers. For the performance
Overview
Module
Components
Module Overview
task, students will be asked to create a magic square using positive and
negative fractions.
1) Scoring Guide
2) Task
Page 1
Least and Greatest
Scoring Guide
Description
The core element of performance required by this task is:
 Choose numbers and operations to give greatest and least results.
Points
Total
Points
1
2
Based on this, credit for specific aspects of performance should be given as follows:
3
1
= 17 (You can accept 17.25)
4
4
1
3
3
Student gives correct answer: ´ - = 2
4
8
1. Student gives correct answer: 18 + -
2. Student gives correct explanation: Multiplying a positive fraction with a negative
fraction will make the rational number closest to zero than multiplying a positive
integer with a negative integer.
OR
Student uses a number line as a diagram of the placement of the product(s).
3. Student gives correct answer: -6 +
Student gives correct answer:
1
1
= -5
2
2
18 ´ -6 = -108
4. Student gives correct explanation: One of the numbers must be the greatest
positive integer and the other number must be the least negative integer.
5. a. Student gives correct answer: 12
b. Student gives correct answer: 15
c. Student gives correct answer: The sum of the squares is 3 times the center
number.
(Credit can be given for correct process, but incorrect arithmetic)
6. Student correctly creates a magic square that:
 includes 9 different numbers/fractions
 sums to 1
 has a center number with a fraction that when multiplied by 3 equals 1
 uses only fractions
 uses positive and negative numbers
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
3
6
TOTAL POINTS:
(possible points = 17 points)
Math Grade 7: Scoring Guide
Page 2
Student Name ______________________
Least and Greatest
1. In this question, make up calculations with answers that are greater than any other
calculation.
For each calculation, you must choose one positive and one negative number from this
list. You can use each number more than once.
3
4
12
-6
18
1
2
2. Explain with words or diagrams how to make sure your multiplication equation is greater
than any other possible equation.
Math Grade 7: Least and Greatest
Page 1
Student Name ______________________
3. Now make the answers in this question make equations with answers that are less than
any other calculation.
For each calculation, you must choose one positive and one negative number from this
list. You can use each number more than once.
3
4
4
12
-6
18
1
2
Explain how to choose numbers to make the answer to a multiplication equation less
than any other equation.
Math Grade 7: Least and Greatest
Page 2
Student Name ______________________
5. Fraction Magic Square
A magic square is an arrangement like the one below where the vertical, horizontal, and
diagonal lines of numbers all add up to the same value. This “same value” is called the
sum of the magic square.
4
1
7
7
4
1
1
7
4
a. What is the sum of this magic square?
Here is another magic square.
8
1
6
3
5
7
4
9
2
b. What is the sum of this magic square?
c. What relationship can you find between the center numbers in the two magic squares
and the sums of the squares?
Math Grade 7: Least and Greatest
Page 3
Student Name ______________________
Performance Task
6. Design a 3  3 magic square with 9 different numbers, like 5b.
Using positive and negative fractions, with at least two different denominators, create a
magic square whose sum is 1. Show your work.
Math Grade 7: Least and Greatest
Page 4