In this unit, your student will be representing situations with diagrams and equations. There are two main categories of situations with associated diagrams and equations.
Here is an example of the first type: A standard deck of playing cards has four suits. In each suit, there are 3 face cards andĀ
and its associated equation could beĀ
Here is an example of the second type: A chef makes 52 pints of spaghetti sauce. She reserves 3 pints to take home to her family, and divides the remaining sauce equally into 4 containers. A diagram we might use to represent this situation is:
and its associated equation could beĀ
Here is a task to try with your student:
Solution:
Diagram A representsĀ
Your student is studying efficient methods to solve equations and working to understand why these methods work. Sometimes to solve an equation, we can just think of a number that would make the equation true. For example, the solution toĀ
An important method for solving equations isĀ doing the same thing to each side. For example, let's show how we might solveĀ
Another helpful tool for solving equations is to apply the distributive property. In the example above, instead of multiplying each side byĀ
Here is a task to try with your student:
Elena picks a number, adds 45 to it, and then multiplies byĀ
Find Elenaās number. Describe the steps you used.
Solution:
Elenaās number was 13. There are many different ways to solve her equation. Here is one example:
This week your student will be working with inequalities (expressions withĀ
Here is a task to try with your student:
Noah already hasĀ $10.50, and he earnsĀ $3 each time he runs an errand for his neighbor. Noah wants to know how many errands he needs to run to have at leastĀ $30, so he writes this inequality:
Ā
We can test this inequality for different values ofĀ
SolutionsĀ
This week your student will be working with equivalent expressions (expressions that are always equal, for any value of the variable). For example,Ā
Row 1 |
Ā | ||
---|---|---|---|
Row 2 | whenĀ |
||
Row 3 | whenĀ |
Ā Ā |
We can also use properties of operations to see why these expressions have to be equivalentāthey are each equivalent to the expressionĀ
Here is a task to try with your student:
Match each expression with an equivalent expression from the list below. One expression in the list will be left over.Ā
List:
Solution
IM 6ā8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6ā8 Math Curriculum is available at https://openupresources.org/math-curriculum/.