7th Grade: Unit 1
Number Systems and Expressions and Equations
7 weeks
The focus of the first two weeks will be to set classroom rules and procedures, and to teach students skills to be used in group work, collaboration, etc. The students will also begin to work on using signed numbers using counters and number lines.
Week #1:
8/27 – Use the following problem as a discussion opener: The digits of a four-digit number are 1, 3, 6, and 9, but not necessarily in that order.
· The tens digit is prime.
· The hundreds digit is three more than the tens digit.
· What is the number?
This day will focus on establishing rules and procedures as well as the basic first day information gathering (information sheets, etc.).
8/28 – Use the following problem as a discussion starter: Susan bought some apples. She gave ½ her apples and ½ and apple to her mom. Then she gave ½ her remaining apples and ½ of an apple to her brother. Then she gave ½ her remaining apples and ½ an apple to her sister. This left her with ¼ dozen apples. How many apples did Susan originally buy?
This day will also include the diagnostic assessment for this unit. The teachers will use the assessment in the Common Core Crosswalk book for the Number Systems and the Expressions and Equations. This should be about 24 questions – 20 multiple choice and 4 open response.
8/29 – Use the following problem as a discussion starter:
This day will also include reviewing the diagnostic assessment.
8/30 – Continuing the week with work on whole and small group discussions; you can use the discussion starter at http://teacher.scholastic.com/maven/pdf/cafeteria_caper.pdf
Week #2: Begins work on 7.NS.1
9/6: Begin to work on understanding of the number line.
Distances on the number line 2
http://illustrativemathematics.org/illustrations/310
On the number line above, the numbers a and b are equidistant from zero. What is a + b? Explain how you know.
9/7: Using counters (manipulatives) for adding signed numbers:
Use integer chips to find the sum of two integers.
The yellow side of an integer chip shows +1 and the red side shows -1. A pair of opposite chips (one red and one yellow) shows 0.
Work together using integer chips to show the first integer in each sum. Then use more integer chips to show the second integer in the sum. Work with other students to make sure each integer is shown correctly.
Then find the sum of the two integers by removing pairs of opposite chips and counting the chips that remain.
1. 5 + (-7) =
2. -2 + 8 =
3. -3 + (-5) =
4. -1 + 8 =
5. 7 + (-4) =
6. 6 + (-6) =
After removing the opposite pairs, how did you decide what integer was shown? Explain your method.
9/8 Continue working on understanding signed numbers with chips and number lines.
A number line is shown below. The numbers 0 and 1 are marked on the line, as are two other numbers a and b.
b 0 1 a
Which of the following numbers is negative? Choose all that apply. Explain your reasoning.
· a– 1
· a– 2
· -b
· a+ b
· a – b
· ab + 1
9/9 Continuing with signed numbers:
We talked about using the video listed on the TN unit. The video is done primarily for teachers. The ideas are great, if you are comfortable rapping, etc. with your students. Certainly watch it and see what you think.
https://www.teachingchannel.org/videos/math-teaching-techniques
The other option would be to use the Grab-A-Charge activity from AIMS. That activity continues the use of the integer chips and reinforcing the development of the rules.