Teaching Priority Concepts in Math Grade 7

Tricia ProficErie 1 BOCES

State Updates Modules 1 and 2 are available online at

engageny.org Link to modules

Annotated State Sample Questions Link to sample questions

Bar Models/Tape Diagrams, Double Number Line Diagrams During their last workout, Izzy ran miles in 15 minutes,

and her friend Julia ran miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct? Use any approach to find the solution.

Table Solution

Bar Model/Tape Diagram

Bar Model/Tape Diagram

Equations

Double Number Line

Multi-Step Ratio Problem (tape diagram)A retail clothing store advertises the following sale: Shorts are off the original price, pants are off the original price and shoes are off the original price. If a pair of shoes cost $40 and is advertised at off the original price, what is the sale price?

Tape Diagram Solution

Rational Numbers Addition of integers using the number line

Counting up and down on the number line Directionality on the number line in terms of a vector

The Integer Game

Object: To get as close to zero as possible Each student is given 4 cards Each turn, a player can choose a card off the discard pile

or from the deck and must discard at the end of their turn

The students play 4 rounds and the student with the score closest to zero wins.

Knowledge of this game is important if you are using the modules because the exit tickets and assessments reference this game.

Subtraction of Negative Numbers Students explore subtracting a negative integer with the

integer game Compare subtracting to removing a negative integer

card Example:

4+ (-2) 4 +(-2) – (-2) 4 + (-2) +2

Removing (subtracting) a negative card changes the score in the same way as adding a card whose value is the additive inverse or opposite.

Distances between Rational Numbers Finding the distance between two numbers using a

horizontal and vertical number line Show the distance broken up into two sections from zero

to each number Define the distance formula as

How do you define “the distance formula”

Multiplication of Integers Integer Game

Students clone a negative integer in their hand to see how it affects their score

Students remove a positive integer in their hand multiple times to see how it affects their score

Students remove a negative integer from their hand to see how it affects their score

Adding a value multiple times has the same effect as removing the opposite value the same number of times

Generalize rules for multiplying integers

Division of Integers Division of integers is generalized to rules

Divide the numbers without the signs to get the absolute value of the quotient

Decide the sign of the quotient positive when the divisor and dividend have the same signs Negative when the divisor and dividend have different sign

Apply properties of operations to multiply and divide rational numbers

Algebraic Solutions vs. Tape DiagramsDuring one rainy day on the vacation, the entire family decided to go watch a matinee movie in the morning and a drive-in movie in the evening. The price for a matinee movie in the morning is different than the cost of a drive-in movie in the evening. The tickets for the matinee morning movie cost $6 each. How much did each person spend that day on movie tickets if the ticket cost for each family member was the same? What was the cost for a ticket for the drive-in movie in the evening?