lesson 2 skills maintenance lesson planner

Unit 9 • Lesson 2 1035

324 Unit9•Lesson2

Name Date

SkillsMaintenanceMultiplyingaPositiveandaNegativeInteger

Activity1

Solvetheproblemsbymultiplyingpositiveandnegativeintegers.

1. 2 · −8 −16

2. 9 · −4 −36

3. 9 · −8 −72

4. −2 · 4 −8

5. 2 · −3 −6

6. −6 · 6 −36

7. 6 · −8 −48

8. −8 · 7 −56

9. 7 · −4 −28

Lesson2 SkillsMaintenance

Skills MaintenanceMultiplying a Positive and a Negative Integer(Interactive Text, page 324)

Activity 1

Students solve multiplication problems with positive and negative integers.

Skills MaintenanceMultiplying a Positive and a Negative Integer

Building Number Concepts: Multiplying Two Negative Integers

We discuss what happens when we multiply two negative integers. It is impossible to demonstrate taking something a negative number of times.

We introduce a structure called PASS for thinking about these kinds of problems. This helps students remember what sign to give the answer when multiplying and dividing integers.

ObjectivesStudents will multiply two negative integers. Students will practice a strategy to remember multiplication rules.

Problem Solving: Drawing Shapes on Coordinate Graphs

Coordinate graphs give us insight into the patterns that are happening numerically when we perform geometric transformations on shapes.

ObjectiveStudents will use coordinates to help draw shapes on a coordinate graph.

HomeworkStudents use PASS to solve integer multiplication problems, give the coordinates of each vertex on the octagon, and tell if the product is correct by responding true or false. In Distributed Practice, students practice addition and subtraction of integers as well as review decimal number and fraction operations.

Lesson Planner

Multiplying Two Negative IntegersProblem Solving: Drawing Shapes on Coordinate Graphs

Lesson 2

1036 Unit 9 • Lesson 2

Lesson 2


How do we multiply two integers?We know that when we multiply two positive integers together, we get a positive answer.

Let’s look at what multiplication with two positive integers looks like on a number line.

Example 1

Multiply two positive integers using a number line.

4 · 5

We see that 4 · 5 = 20.

In the last lesson, we learned that multiplying a positive number and a negative number gives a negative answer. Let’s see what this looks like on a number line.

Example 2

Multiply a positive and a negative integer using a number line.

3 · −7

We see that 3 · −7 = −21.

−20 −15 −10 −5 0 5 10 15 20

1 time 2 times 3 times 4 times

−28 −21 −14 −7 0 7 14 21 28

3 times 2 times 1 time

Multiplying Two Negative Integers

Multiplying Two Negative IntegersProblem Solving: Drawing Shapes on Coordinate Graphs

Lesson 2

that this is just like repeated addition of 5 four times: 5 + 5 + 5 + 5 = 20.

• Next show the problem 3 · −7 and the number line from Example 2 . Make sure students see that this problem involves multiplying positive and negative integers.

• Remind students that we can show this on a number line if we remember to move in a negative direction. Show how we take 3 units of 7 and move in the negative direction to get the answer of −21.

Building Number Concepts: Multiplying Two Negative Integers

How do we multiply two integers?(Student Text, page 637)

Connect to Prior KnowledgeRemind students that we already know what multiplying positive integers looks like. We can do this on a number line. Have students come up to the board and demonstrate examples of integer multiplication using a number line.

Link to Today’s ConceptTell students that today we learn a strategy to multiply two negative integers.

DemonstrateEngagement Strategy: Teacher ModelingDemonstrate how to multiply integers in one of these ways:

: Use the mBook Teacher Edition for Student Text, page 637.

Overhead Projector: Display Transparency 6, and modify as discussed.

Board: Draw a number line on the board, and modify as discussed.

• First show Example 1 , which shows multiplication between two positive integers.

• Show the number line, and help students observe the intervals of 5 units in the number line.

• Make sure students understand that the problem 4 · 5 involves taking 5 four times. Remind students that we move to the right in a positive direction because both numbers are positive. We count out each unit of 5 until we reach 20. Remind students

637



Lesson 2

What is the product of two negative integers?What kind of answer do we get when we multiply two negative integers? There are only two choices: The answer can be positive or negative. So what happens when we work −9 · −2 on a calculator? We get 18.

The answer is positive. There is no easy way to explain why multiplying two negative integers gives a positive answer.

With multiplication of positive and negative integers, we know whether the answer is going to be positive or negative by remembering two simple rules.

Multiplication Rules

Multiplication Rule 1

If the signs are the same, 9 · 2 = 18 the answer is positive. −9 · −2 = 18

Multiplication Rule 2

If the signs are different, −9 · 2 = −18 the answer is negative. 9 · −2 = −18

We will use the same rules when we divide with negative numbers.

The product of two negative integers is a positive number.

What is the product of two negative integers?(Student Text, page 638)

Demonstrate• Turn to Student Text, page 638, and read

the material. Now we come to the dilemma of a negative times a negative. If possible, have students take out a calculator and multiply −9 · −2. The answer is 18, which is a positive number.

• Tell students we have to have rules for problems like these that we cannot show with a model like a number line or a picture.

• Have students look at the two rules at the bottom of the page. Multiplication Rule 1 states that if the signs of the numbers are the same, the product will be positive. Multiplication Rule 2 states that if the signs of the numbers are different, the answer will be negative.

• Explain that we use these rules to divide negative numbers as well. Emphasize Rule 1, especially in the context of negative numbers. Students may have difficulty grasping this concept, believing that two negatives should equal a negative number.

DiscussCall students’ attention to the Power Concept, and tell them that it will be helpful as they complete the activities.

The product of two negative integers is a positive number.

638


Lesson 2


Lesson 2

How do we remember the multiplication rules?Here is a simple way to remember the rules for multiplying and dividing integers. One word helps keep them straight: PASS.

Positive

Answers

Same

Sign

Just remember PASS. When we look at a multiplication problem with negative numbers, we ask ourselves if the signs are the same. If they are, the answer will be positive. If not, the answer will be negative.

Reinforce UnderstandingUse the mBook Study Guide to review lesson concepts.

Apply SkillsTurn to Interactive Text, page 326.

Reinforce UnderstandingIf you feel students need more practice with remembering the multiplication rules, have them solve the following multiplication problems:

8 · 4 (32)

−3 · −5 (15)

2 · −1 (−2)

9 · −9 (−81)

−9 · −9 (81)

How do we remember the multiplication rules?(Student Text, page 639)

ExplainExplain to students that the rules we just learned might be confusing and difficult to remember. That is why we introduce a way for students to remember the rules a little more easily. We call it PASS.

We use this acronym as a way to help students remember what is otherwise a nonintuitive set of rules. Read through PASS with students on page 639 of the Student Text. Make sure they see that if the signs are the same, the answer is always positive.

Check for UnderstandingEngagement Strategy: Look About

Write these problems on the board or overhead:

−2 · −4 (+)

−6 · 12 (−)

−11 · 10 (−)

4 · 6 (+)

−3 · −7 (+)

Tell students that they will determine whether the answer is positive or negative for each problem with the help of the whole class. Tell students they are not to solve the problems. Students should write either + or − in large writing on a piece of paper or a dry erase board after you point to each problem. When students finish, they should hold up their answers for everyone to see.

If students are not sure about the answer, prompt them to look about at other students’ solutions to help with their thinking. If time allows, go through the actual multiplication with students.

639


Unit9•Lesson2 325

Name Date

Uni

t 9

ApplySkillsMultiplyingNegativeIntegers

Activity1

Usethemultiplicationrulestotelliftheanswersarepositiveornegative.Circletheanswer.

1. 235 · −8 Positive or Negative

2. −35 · −81 Positive or Negative

3. 207 · 9 Positive or Negative

4. −415 · −10 Positive or Negative

5. 5 · −329 Positive or Negative

6. −287 · 3 Positive or Negative

Activity2

Completethemultiplicationproblemswithpositiveandnegativeintegers.

1. −2 · −8 = 16 2. 7 · 8 = 56

3. −6 · −3 = 18 4. −9 · 8 = −72

5. −4 · −7 = 28 6. −5 · 5 = −25

7. −6 · −6 = 36 8. 4 · 9 = 36

9. −6 · 9 = −54 10. −2 · −3 = 6

11. 6 · −4 = −24 12. −9 · 7 = −63

Lesson2 ApplySkills

Apply Skills(Interactive Text, page 325)

Have students turn to page 325 in the Interactive Text, which provides students an opportunity to practice integer multiplication.

Activity 1

Students circle the answer that tells if the product is positive or negative. Remind them to use PASS rules.

Activity 2

Students solve a mix of integer multiplication problems. These are all basic facts, so a calculator is not required. We want students to practice using the PASS rules for determining the sign of the answer.

Monitor students’ work as they complete the activities.

Watch for:

• Can students determine the correct sign of the answer?

• Can students solve the basic fact?

• Do students remember and implement the PASS rules?

Reinforce Understanding Remind students that they can review lesson concepts by accessing the online mBook Study Guide.


Lesson 2


Lesson 2

How do coordinates help us draw shapes on a coordinate graph?

We use x-coordinates and y-coordinates on a coordinate graph to draw objects. We have drawn objects on graph paper by measuring distances or counting squares. Now we will draw the objects on coordinate graphs. The main difference is that we will use coordinates to describe the vertices, or corners, of the shapes.

Example 1

Place a triangle on a coordinate graph using the coordinates of its vertices.

Let’s say that the designers at Crash Bang Entertainment want to draw a triangular spaceship.

The designers measure the spaceship so they can put it on a coordinate graph.

A C

B

7 2

3

To make the designing easier, the designers use just the basic triangle outline on the coordinate graph. They label the vertices, or corners, A, B, and C. The coordinates of A, B, and C are:

A = (1, 3)

B = (8, 6)

C = (10, 3)



How do coordinates help us draw shapes on a coordinate graph?(Student Text, pages 640–641)

Connect to Prior KnowledgeRemind students that they already drew objects on graph paper by measuring distances and counting squares.

Link to Today’s ConceptToday we learn to draw objects based on their coordinate points.

Demonstrate• Look at Example 1 on page 640 of the

Student Text, and read the spaceship design scenario. Point out that the basic design of the spaceship is a triangle.

• Point out the triangle and coordinates of the vertices. Explain to students that we use these coordinates to draw the triangular shape on a coordinate graph.

640



Lesson 2

The triangle is placed on the coordinate graph like this:

87

6

5

432

1

–1

–2

–3

–4

–5–6

–7–8

1 2 3 4 5 6 7 8–8–9–10 –7–6 –5 –4 –3–2 –1

y

x9 10

B (8, 6)

C (10, 3)A (1, 3)

Coordinates help us draw shapes on a grid. We only need to know the vertices. We draw line segments between the points to finish the shape.

Problem-Solving ActivityTurn to Interactive Text, page 326.

Reinforce UnderstandingUse the mBook Study Guide to review lesson concepts.

Demonstrate• Turn to page 641 of the Student Text,

and continue going over Example 1 with students. Demonstrate how to put the triangle on a coordinate graph. Because we know the coordinates of each of the vertices, we can plot them on the graph.

• Help students observe that there are three coordinate points, and each one represents a vertex. Triangles have three vertices, so the shape must be a triangle.

• Show students how to plot each coordinate on the graph, then draw line segments to connect the vertices.

641


Lesson 2

326 Unit9•Lesson2

Name Date

Problem-SolvingActivityDrawingShapesonCoordinateGraphs

Nowit’syourturntousecoordinatestodrawashape.Drawthetrapezoidonthecoordinategraph.Startthedrawingbyplacingthecoordinatesonthegraph.Thenconnectthepointstomaketheshape.

8

7

6

5

43

21

–1

–2

–3

–4

–5–6

–7–8

1 2 3 4 5 6 7 8–8 –7–6 –5 –4 –3–2 –1

y

-y

x-x

B C

DA

A: (0, 1) B: (1, 5)

C: (4, 5) D: (6, 1)

Lesson2 Problem-SolvingActivity

ReinforceUnderstandingUse the mBook Study Guide to review lesson concepts.

Problem-Solving Activity(Interactive Text, page 326)

Have students turn to page 326 in the Interactive Text, which provides students an opportunity to practice graphing shapes on a coordinate graph.

Students draw a trapezoid on the coordinate graph first by plotting the coordinates of the vertices. Then they connect the lines and create the shape.

Monitor students’ work as they complete the activity.

Watch for:

• Can students accurately plot the vertices?

• Can students draw the lines and create the trapezoid?

Be sure to go over students’ answers when they complete the activity. It is important that they begin to observe patterns informally in the coordinates of the vertices. We take a more formal look at these patterns later in the unit.

Reinforce Understanding Remind students that they can review lesson concepts by accessing the online mBook Study Guide.



Lesson 2

Activity 1

Use PASS rules to solve the problems.

1. −3 · 9 −27 2. 4 · −8 −32 3. −6 · −7 42 4. 8 · −6 −485. −5 · 5 −25 6. −6 · −4 24 7. 9 · −3 −27 8. −2 · −2 49. −9 · 7 −63 10. 4 · 5 20

Activity 2

Identify the x- and y-coordinates for each letter on the graph. On your paper, label the coordinates with the letters given.

Activity 3

Tell if the answer is true or false.

1. −4 · −3 = −12 False 2. 7 · −4 = −28 True 3. −7 · 5 = −35 True4. −7 · −11 = 77 True 5. −8 · 9 = 72 False 6. −6 · −6 = −36 False

Activity 4 • Distributed Practice

Solve.

1. −5 − −8 3 2. 14 − 9 5 3. 15 + −7 8 4. −14 + −21 −355. 0.71 · 0.2 0.142 6. 1.25 − 0.98 0.27 7. 7

8 ÷ 14 31

2 8. 89 − 2

3 29

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

1 2 3 4 5 6 7 8–8 –7 –6 –5 –4 –3–2 –1

y

x

A

BC

D

HE

GF

A: (7, 4) C: ( −2, 7) E: ( −5, −3)G: (4, −6)

B: (4, 7) D: ( −5, 4) F: ( −2, −6) H: (7, −3)

Homework

Homework

Go over the instructions on page 642 of the Student Text for each part of the homework.

Activity 1

Students solve a mix of integer multiplication problems using PASS rules.

Activity 2

Students find the coordinates of each of the vertices on the octagon.

Activity 3

Students tell if the product is correct. They respond true or false.

Activity 4 • Distributed Practice

Students practice addition and subtraction of integers, as well as review decimal number and fraction operations. 642

lesson 2 skills maintenance lesson planner

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