This week your student will be learning to visualize, write, and solve equations. They did this work in previous grades with numbers. In grade 6, we often use a letter called a variable to represent a number whose value is unknown. Diagrams can help us make sense of how quantities are related. Here is an example of such a diagram:
Since 3 pieces are labeled with the same variable
A solution to an equation is a number used in place of the variable that makes the equation true. In the previous example, the solution is 5. Think about substituting 5 for
Solving an equation is a process for finding a solution. Your student will learn that an equation like
Here is a task to try with your student:
Draw a diagram to represent each equation. Then, solve each equation.
Solution:
This week your student is writing mathematical expressions, especially expressions using the distributive property.
In this diagram, we can say one side length of the large rectangle is 3 units and the other is
This is an example of the distributive property.
Here is a task to try with your student:
Draw and label a partitioned rectangle to show that each of these equations is always true, no matter the value of the letters.
Solution:
Answers vary. Sample responses:
This week your student will be working with exponents. When we write an expression like
Here is a task to try with your student:
Remember that a solution to an equation is a number that makes the equation true. For example, a solution to
List:
Solution:
This week your student will study relationships between two quantities. For example, since a quarter is worth 25?, we can represent the relationship between the number of quarters,
We can also use a table to represent the situation.
1 | 25 |
---|---|
2 | 50 |
3 | 75 |
Or we can draw a graph to represent the relationship between the two quantities:
Here is a task to try with your student:
A shopper is buying granola bars. The cost of each granola bar is $0.75.
Solutions
IM 6–8 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 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.