Unit 7, Lesson 9
Working with Signed Numbers
Extra Support Materials for Algebra 1
9.1
Warm-up
Standards Alignment
Building On
Addressing
7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Building Toward
HSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it. For example, see as , thus recognizing it as a difference of squares that can be factored as .
Instructional Routines
Worked ExampleMaterials
NoneActivity Narrative
The purpose of this activity is to model using a diagram to multiply numbers represented by 10 plus or minus a value.
This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.
Launch
Arrange students in groups of 2. Tell them to close their books or devices (or to keep them closed). Reveal the prompt and the first step. Give students a brief quiet think time, and ask them to give a signal when they have read the step and are ready to see the next. Once most students have given the signal, reveal the next step. Repeat until all steps have been revealed.
If previous work indicates that most students will struggle to make sense of a step, pause and give students 1 minute to discuss with their partner and formulate a question about the step. Ask 1–3 groups to share their questions, inviting other groups to answer while recording responses next to the step for all to see. Once questions have been answered, continue to the next reveal.
Action and Expression: Internalize Executive Functions. To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization
Supports accessibility for: Memory, Organization
Activity
NoneSolve using a diagram.
Step 1:
| 10 | 4 | |
|---|---|---|
| 10 | ||
| -2 |
Step 2:
| 10 | 4 | |
|---|---|---|
| 10 | 100 | 40 |
| -2 | -20 | -8 |
Step 3:
Activity Synthesis
The purpose of this discussion is to see how the diagrams students have been using can be used to approach problems in other ways. Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.
- “How does this diagram represent the problem ?” ( and , so the same numbers are being used, they are just split into other pieces.)
- “How does a negative number change how the diagram is used?” (Instead of adding all of the numbers some are subtracted because adding a negative number is the same as subtracting a positive number.)
- “How could we check the answer from the diagram to make sure it is correct?” (We could use another diagram with a different split (for example, and ), use a tool like a calculator, or use one of the other multiplication methods we know.)
Ask partners to compare their responses to each question and decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.
If time allows, consider displaying a second worked example next to the first that either:
- Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7).
- Shows the same method with an error that students can critique and correct (MP3).
9.2
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
The purpose of this activity is to explore how multiplying positive and negative numbers affects the product, while writing solutions in expanded form. In the associated Algebra 1 lesson, students multiply monomials and binomials to write quadratic equations in standard form. Students reason abstractly and quantitatively when rewriting equations in another form (MP2).
Launch
Recall that one way to find is by rewriting it as , and drawing a diagram like this to organize the terms: or . We can refer to expressions like this as “expanded form.”
| 10 | 4 | |
| 10 | ||
| 1 |
Tell students that we can still use these diagrams to help with expanding and factoring when negative numbers are involved, by rewriting expressions involving subtraction like using addition, like .
9.3
Activity
Materials
NoneActivity Narrative
This activity is an opportunity for students to practice rewriting expressions using the distributive property.
The row with is designed to allow students to figure out how to factor by reasoning based on structure they have already studied. The rows with and are designed to show how combining like terms is an application of the distributive property.
In this partner activity, students take turns writing equivalent expressions. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.