Lesson Plans for Melanie Keith-Hayes 7 th Grade Math

Transcription

1 Monday Tuesday Wednesday Thursday Friday Week ATN C Comparing Integers (Do c first and draw INTRO CHART ATN c Adding Integers Integers Homework 19 ATN c Subtracting Integers 20 ATN c Multiplying Integers

2 Accentuate the Negative Investigation 1, Problem 1.3 What s the Change? Using a Number Line Model Mathematical Goals Write number sentences to reflect the actions and results of changes in situations and find missing values Develop and use a number line model for representing addition and subtraction State Standards 7.2C Vocabulary: Materials: Transparency 1.3, Number Lines labsheet, Labsheet 1.3 MSPLabsheet 1ACE Exercises 31 and LAUNCH (10 minutes) Teacher Notes Engage students in a discussion of temperature changes they may have experienced. Using the context presented in the problem, help students understand that these changes have both distance and direction. In the first example, what does the 4 represent? What does the + 45 represent? In the second example, why does n equal 14? Have students begin working individually, and then have them work with partners. 2. EXPLORE (20 minutes) Teacher Notes As you circulate, have students explain how they are determining their solutions. Encourage students to write addition and/or subtraction number sentences to describe their work. 3. SUMMARIZE (15 minutes) Teacher Notes Have students demonstrate and explain their solutions. Take time to consider the number sentences that can be written to describe the actions. When you wrote addition sentences, what did the first addend represent? What did the second addend represent? What did the sum represent? In thinking about addition number sentences, it may be helpful

3 to describe the actions as: Starting Temp. + Change in Temp. = Resulting Temp. The change will have both distance and direction. Companion subtraction number sentences that are relevant in some of the problems can be generalized in the same way. When you wrote subtraction sentences, what did the numbers represent? Resulting Temp. - Starting Temp. = Change in Temp. OR Resulting Temp. - Change in Temp. = Starting Temp.

4 Accentuate the Negative Investigation 2, Problem 2.1 (1.5 days) Introducing Addition of Integers Introducing Addition of Integers Mathematical Goals Develop algorithms for adding integers Model addition of integers using distance/direction on a number line and a chip model Observe that the Commutative Property holds for addition of rational numbers State Standards 7.2C; 7.15A Vocabulary: Materials: labsheet, commutative property Transparencies 2.1A, 2.1B, Chips or tiles in two colors, Number Lines Small Chip Boards labsheet, Labsheet 2.1MSP 1. LAUNCH (10 minutes) Teacher Notes Show the first problem on an overhead, separate from the text. How could you model this problem using chips? Focus on the actions of the problem and how chips can model these actions. Show the second problem, separate from the text. How could you use a number line to model this problem? Have students talk through using a number line (make sketches) to show the solution. How is this problem different from the one before? Have students work with partners. Do both models but only do first 2 of each group 2. EXPLORE (20 minutes) Teacher Notes Suggest they use what they know about working with chips and the number line to help them reason about the problems. To help students generalize, ask: How do you know if the solution will be positive or negative?

5 3. SUMMARIZE (15 minutes) Teacher Notes Have different teams present their solutions to Question A. How do you compute problems in which both signs are the same? The signs of the numbers are different? When appropriate, have students make up stories for the problems so that their solutions can be tied back to a context. Discuss similarities between problems to help students to a general algorithm. For what types of problems did you get a negative number? For Question A, part (3), post several problems that students have made. For Question B, have students post several possibilities. Writing mathematical sentences will help their understanding of equality needed for further work. How can you make a sum that results in exactly 5? For Question C, have students share stories for the problems. Which model chip or number line can represent (a given story)? Question D explores the Commutative Property to see whether it holds for addition with negative numbers. It does. Going Further Compute the following = 7

6 Accentuate the Negative Investigation 2, Problem 2.2 (1.5 days) Introducing Subtraction of Integers Mathematical Goals Develop algorithms for subtracting integers Model subtraction using distance/direction on a number line and a chip model Observe that the Commutative Property does not hold for subtraction of rational numbers State Standards 7.2C; 7.15A Vocabulary: absolute value Materials: Transparencies 2.2A, 2.2B, Chips or tiles in two colors, Number Lines labsheet, Small Chip Boards labsheet, Labsheet 2.2 MSP 1. LAUNCH (10 minutes) Teacher Notes Show the first problem on an overhead, separate from the text. Focus on the actions of the problem and how chips can be used to model these actions. In the second situation, students need to represent + 5 so that + 7 can be removed. Model the actions and write mathematical sentences that reflect the changes made. You may want to model a few other problems as well. Show the second problem, separate from the text. Have students show the solution using a number line (make sketches). Discuss that the measure of distance is always positive. The sign of the answer tells you direction. Have students start Question A individually and then move to small groups to discuss their findings. 2. EXPLORE (20 minutes) Teacher Notes Suggest students use what they know about working with chips and the number line to help them reason about the problems in the two groups. Once students make sense of Question A, move on to Questions B and C. 3. SUMMARIZE (15 minutes) Teacher Notes Have different teams present their solutions to Question

7 A. How do you compute problems in which both signs are the same? The signs of the numbers are different? When appropriate, have students make up stories for the problems so that their solutions can be tied back to a context. Discuss similarities between problems to help students to a general algorithm. How do you know if the difference is positive or negative? When you are subtracting with integers, must you always think of the operation as subtraction? Why or why not? For Question B, post and organize several problems that students have made (categories: both positive numbers, both negative numbers, or one positive and one negative). Discuss ways problems can be structured to produce the solutions. For Question C, have students focus on the Commutative Property. Check for Understanding Without computing the answers, predict how the answers in each pair will compare. Will the answers be the same or different? If they are different, which will be greater? Explain and and 4 12

8 Accentuate the Negative Investigation 3, Problem 3.1 Introducing Multiplication of Integers Mathematical Goals Use a number line/motion model to develop the relationship between repeated addition and multiplication with integers Develop and use algorithms for multiplying integers Vocabulary: Materials: 25 parts (a) MSP Transparency 3.1, Number Lines Labsheet, Labsheet 3ACE Exercise and (b), Labsheet 3ACE Exercise 25 parts (c) and (d), Labsheet 3.1 State Standards 7.2ABC Local Standards 7 Exam Obj. #4 & 9 6 th H Exam Obj. #18 1. LAUNCH (10 minutes) Teacher Notes Look at the Did You Know? Explain the Number Relay race. Have students walk through a simulation. Ask clarifying questions to make sure students understand. How far does each racer run? Explain the first leg of the relay. Do the first problem in Question A with them. What does 5 meters per second mean? Which way is he running? Left or right? Positive or negative? What number sentence could you write to show where Hahn will be 10 seconds later? What do the 5 and the 10 stand for? Suppose Hahn were running 5 meters per second to the left. How would this change the number sentence? What do the 5, 10, and 50 indicate? Work in pairs and then move to groups of four for further discussion. Discuss Some notes on Notation on page 42. At this point the book will no longer raise the negative sign. 2. EXPLORE (20 minutes) Teacher Notes Make sure they are writing complete mathematical sentences. If students are struggling, summarize Question A before going on to Question B. 3. SUMMARIZE (15 minutes) Teacher Notes Have students share their number sentences for

9 Question A. Analyze how the addition and multiplication sentences are related. With part (2), ask: What number sentences did you write for part (2)? What does 5 x 4 mean? What does multiplication mean? Draw students attention to patterns with the combinations of positive and negative signs. For Question A part (3): What number sentences did you write for part (3)? Here you have a positive times a negative. Why is the result negative? What does 8 x ( 6) mean? As students describe their number sentences, note the sign patterns. In Question A part (5), you have a negative direction and a negative time. Why does it make sense that this means Tori is at a positive position on the racing field? Have students present their algorithms. What is happening when you multiply a positive number by a negative number? A negative times a negative? Discuss exponents with negative bases ( b) x Going Further If you had a negative times a negative times a negative, would the results be negative or positive? Is multiplication commutative for negative numbers?

10 (7.1 A) compare and order integers and positive rational number (7.2 C) use models, such as concrete objects, pictorial models, and number lines, to add, subtract, multiply, and divide integers and connect the actions to algorithms;