General Information
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Associative Property
- Commutative Property of Multiplication
- Division Property of Equality
- Equation
- Identity Property of Multiplication
- Integer
- Multiplicative Inverse (reciprocal)
- Multiplication Property of Equality
- Number Line
- Substitution Property of Equality
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 5, students wrote and evaluated numerical expressions with positive rational numbers. Students also wrote equations to determine an unknown whole number. In grade 6, students extend their understanding to solve one-step equations which include integers. In grade 7, students write and solve one-step inequalities and two-step equations involving rational numbers.- When students write equations to solve real-world and mathematical problems, they draw on meanings of operations that they are familiar with from previous grades’ work.
- Problem types include cases where students only create an equation, only solve an equation and problems where they create an equation and use it to solve the task. Equations include variables on the left or right side of the equal symbol.
- For multiplication, instruction includes the use of coefficients, parentheses and the raised dot symbol (·).
- Use models or manipulatives, such as algebra tiles, bar diagrams and balances to conceptualize equations (MTR.2.1).
- Algebra Tiles
2 = −6
- Bar Diagrams
2 = −26
- Balance
2 = −10
- Instruction includes many contexts involving negative integers, including connections to ratio, rate and percentage problems in MA.6.AR.3.4 and MA.6.AR.3.5.
- Instruction can include students identifying the properties of operations and properties of equality being used at each step toward finding the solution. Explaining informally the validation of their steps will provide an introduction to algebraic proofs in future mathematics (MTR.5.1).
- Students should be encouraged to show flexibility in their thinking when writing equations.
Common Misconceptions or Errors
- Students may incorrectly apply an operation to a single side of an equation.
- Students may incorrectly use the multiplication and division properties of equality on the same side of the equal sign while solving an equation. To address this misconception, use manipulatives such as, algebra tiles, number lines or bar diagrams to show the balance between the two sides of an equation (MTR.2.1).
Strategies to Support Tiered Instruction
- Instruction includes identifying unknowns, constants, negative values, and mathematical operations in the provided context.
- Teacher provides opportunities for students to comprehend the context or situation by engaging in questions such as:
- What do you know from the problem?
- What is the problem asking you to find?
- Are you putting groups together? Taking groups apart? Or both?
- Are the groups you are working with the same sizes or different sizes?
- Can you create a visual model to help you understand or see patterns in your problem?
- Teacher provides opportunities for students to use algebra tiles to co-solve provided equations with the teacher without the need of writing the equation first.
- Teacher provides opportunities for students to co-write an algebraic equation with the teacher without requiring students to solve the equation.
- Teacher models the use of manipulatives such as, algebra tiles, number lines or bar diagrams to show the balance between the two sides of an equation.
Instructional Tasks
Instructional Task 1(MTR.4.1, MTR.7.1)- A solar panel generates 200 watts of power each hour. A warehouse wants to generate 34,000 watts of power each hour.
- Part A. Write an equation to find how many solar panels the warehouse will need on its roof to generate 34,000 watts of power each hour.
- Part B. Explain why you wrote the equation the way you did. Could you write the equation in another way?
- Part C. Find the solution to your equation.
- Part D. What does the solution to your equation mean?
Instructional Items
Instructional Item 1- An outlet mall has 4 identical lots that can hold a total of 1,388 cars. The equation 4 = 1388 describes the number of cars that can fit into each lot. How many cars can fit into each lot?
Instructional Item 2
- Given = 56, what is the value of
?x
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.