Grade 7 Unit 1
7.NS.1
Accentuate the Negative
Lesson 2.1
Addition of Integers p. 22 - 24
In Grade 6 students learned that negative numbers exist. Now students will work on the arithmetic of positive and negative numbers, beginning with addition. Research shows that teaching students a rule (such as “same sign sum”) does not transfer long term across the years of math learning. Teachers are strongly encouraged to avoid teaching rules but instead to give students ample opportunities to make meaning of the mathematics – first from a place of concrete experience, gradually moving to more abstract concepts and algorithms.
Today students subtract using positive and negative whole numbers. The chip method in the book is proven to be useful for student understanding of the meaning of the mathematics. Do not skip it.
7.NS.1
Accentuate the Negative
Lesson 2.2
Subtraction of Integers p. 24 - 27
7.NS.1
Illustrative Math: Difference of
Integers
Addition and subtraction on a number line
7.NS.1
Illustrative Math: Comparing Freezing
Points
Addition and subtraction of positive and negative fractions and decimals.
7.NS.1
Accentuate the Negative
Lesson 2.3 p. 28 – 29
The expectation of the standards is that in addition to the ways presented in the book, students will use number lines to represent addition of positive and negative numbers. The Illustrative Math task listed for today’s activity in the column to the left is a good number line activity.
So far the students have worked primarily with positive and negative whole numbers. Be sure to require students to apply this understanding to addition and subtraction of positive and negative fractions and decimals . The task listed to the left is a good one to use. While it may not take two days, two days are allotted in case you need to scaffold and review.
Students begin to codify their understanding of addition and subtraction of signed numbers. Today they will look for patterns and begin to think about rules that apply. Teachers are encouraged to ask students to answer questions such as:

Is a positive number plus a positive number always, sometimes or never positive?

Is a negative number plus a negative number always, sometimes or never positive?

Is a positive number plus a negative number always, sometimes or never positive?

Grade 7 Unit 1
7.NS.1
Accentuate the Negative
Lesson 2.4 p. 30
7.NS.1
Illustrative Math: Distance Between
Houses
7.NS.1
Engage NY
Module 2
Lesson 8
Students use fact families related to addition and subtraction of signed numbers to expand their understanding of equivalence.
This task requires students to either subtract the smaller number from the larger, or take the absolute value of the difference in any order.
7.NS.2
Accentuate the Negative
Lesson 3.1 p. 44 - 45
Students should be ready to apply the properties of operations to practice what they have been learning about adding and subtracting signed numbers. Lesson
8 of Module 2 of Engage NY has many appropriate problems. If you plan to do all of them, you will need two days. As this lesson ends the work on addition and subtraction, you may want to use a formative assessment on Day 10.
Here is a link to some smarter balanced sample items associated with the middle school standards.
To find the 7.NS.1 questions, under Grade 7, select the Number
System link.
Students now move to multiplying signed numbers. You may want to start the lesson by asking students to find the product of 26 x 13 all the ways they can.
In elementary school, some of the ways students learned about multiplication included area models , skip counting , and skip counting on a number line.
You should expect to see all of these representations. The authors of the text book base this lesson on skip counting on a number line. After the warm-up students should be ready to access the lesson.
Students look at patterns of products of signed numbers in this lesson. They may begin to hypothesize that a negative times a negative is a positive and a negative times a positive is a negative.
7.NS.2
Accentuate the Negative
Lesson 3.2 p. 46
7.NS.2
Illustrative Math: Why is a Negative
Times a Negative Always Positive?
7.NS.2
Accentuate the Negative
Lesson 3.3 p. 47 – 48
This task focuses on the product of negative numbers and the distributive property. Recommend beginning the lesson reviewing the distributive property with positive whole numbers before starting the task.
Students now divide signed numbers. The textbook uses fact families and math sentences to bridge the connection between multiplication and division.

7.NS.2
Accentuate the Negative
Lesson 3.4 p. 48 – 49
7.NS.2
Engage NY
Module 2, Topic B, Lesson 15
7.NS.2
Mars Tasks
Division
7.NS.2
Formative Assessment
7.EE.1
Accentuate the Negative
Lesson 4.1 p. 60 – 63
7.EE.2
Accentuate the Negative
Lesson 4.2 p. 64 – 65
Grade 7 Unit 1
In this lesson students play a game that deepens and applies their understanding of the relationship between multiplication and division of signed numbers. Questions C and D on p. 49 are good examples of this relationship.
Thus far in this unit, students have worked primarily with signed whole numbers. For experience with signed fractions, and decimals, the lesson at left from Engage NY is recommended. In it students multiply and divide positive and negative fractions and decimals. You may want to spend a short amount of time scaffold students toward the work by reviewing multiplication and division of positive fractions and decimals.
This problem indicates the breadth and depth of the CCSS design. Students are asked to make sense of a division answer provided by a calculator. As interpreting a calculator answer is probably new for most students, they will likely also need additional practice with this skill. Recommend allotting 2 days.
Students are now winding up their work on multiplication and division of rational numbers. This is a good time for a short formative assessment.
This should be review for students. Students have been using grouping symbols since Grade 5. Students spent time on the order of operations in Grade 6.
Connecting these notions to positive and negative numbers is the new learning.
For an SBA question idea, use this link and select the Grade 7
Number System question. Note: this question includes a reference to a Grade 6 standard. For an
Engage NY assessment idea, use this link and scroll to p.160.
Students already know a good bit about the Distributive Property. The goal of this lesson is to use the Distributive Property to write equivalent expressions as the Common Core State Standards place a very high value on equivalence.
Rewriting expressions and equations in equivalent form is relatively new for students and the answers may not look like what students have come to expect an answer to look like. This is a big milestone in student math learning.

7.NS.3
Accentuate the Negative
Lesson 4.3 p. 66 – 67
Review
Test
Grade 7 Unit 1
While the student have already learned about multiplying by a negative number, the books’ treatment of the very abstract concept of distributing a negative is both very good and very important.
Omit question E on p. 67 as students have not yet learned about percents.
Several days are allowed here in case time was lost somewhere during this unit.
Recommend spending two days at the most on review.
Several days are allowed here in case time was lost somewhere during this unit.
Recommend not spending more than a day on an assessment.