Moving with Algebra Sampler

12 Step 5b Structured Lesson Plans The Lesson Plans section of the Teacher Manual contains everything the teacher needs to do and say for each lesson , so teachers who need to strengthen their own math skills are provided with daily professional development. SkillBuilders 6-4 Lesson Plans 245 ©MathTeachersPress, Inc. Reproduction by anymeans is strictly prohibited. 19 Subtracting a number gives the same result as adding its opposite. – 5 – 2 – 5 –2 = – 7 There are not any black cubes. Add 2 black and 2 white cubes so you can subtract. Subtract 2 black cubes. There are 7 white cubes left. Shortcut:Add the opposite of the number being subtracted. – 5 – 2 – 5 + ( – 2) = – 7 The opposite of 2 is – 2 Write the opposite of eachnumber. 1. 7 _________ 5. 0 __________ 2. – 5 _________ 6. _________ 3. 2 __________ 7. – _________ 4. – 4 __________ 8. – 2.5 ________ 9. 4– ( – 2) __________ = ____ 12. – 4 – 6 __________ = ____ 15. – 6 – 6 __________ = ____ 18. – 3 – ( – 1) __________ = ____ 10. – 2 – 3 __________ = ____ 13. 5 – ( – 1) __________ = ____ 16. 5 – 0 __________ = ____ 19. – 4 – ( – 5) __________ = ____ 11. – 5 – ( – 2) __________ = ____ 14. – 3 – 4 __________ = ____ 17. – 4 – 2 __________ = ____ 20. – 12 – 5 __________ = ____ Rewrite each subtraction problem as an additionof opposites.Solve. 4+ 2 6 Which sentence is nottrue? A – 2 – ( – 7) = – 9 C 7 – 4 = 3 B – 2 – 6 = – 8 D 4 – ( – 3) = 7 AddingOpposites:AShortcut forSubtraction -7 5 -2 4 0 – 3 4 3 1 2.5 -5 -3 -10 6 -7 -12 5 -6 -2 1 -17 -2+ -3 -5+ 2 -4+ -6 5+ 1 -3+ -4 -6+ -6 5 -0 -4+ -2 -3+ 1 -4+5 -12+ -5 Objective: To subtract integers by adding the opposite. Materials: Black and white cubes (or positive and negative integer squares, Master 19), clear jar, 6-sided dice (two colors) Finding a Pattern In these activities students represent the minuend with black and white cubes in a clear jar and are then asked if there are enough integers to remove the subtrahend. When there are not enough integers to subtract, students will suggest that an equal number of black and white cubes may be added so there will be enough. Students will make a table showing each example and be guided to discover the pattern of adding the opposite as they discuss possible patterns in small groups. Write the following table on the board: ______________________________________________ OriginalNumber No. being subtracted Difference ______________________________________________ 4 – 3 7 – 5 – 2 – 3 – 4 1 – 5 – 3 – 4 1 2 – 2 4 Divide the class into small groups. Give each group a set of black and white cubes to solve the problems. To find a pattern for subtracting integers, solve the problems with models and record the results in a table. Discuss the solutions in your group to see if you can find the pattern for subtracting integers. The pattern should be written in a complete sentence. To show 4 – ( – 3), place 4 black cubes in a jar. How can we remove three white cubes when there are none here? ( add 3 pairs of zero, i.e., 3 black cubes and 3 white cubes, to the jar) Record the difference of + 7. + 4 – ( – 3) = + 7 Pattern: To subtract integers, add the opposite of the number being subtracted. Alternatively, use positive and negative integer squares or write + and — signs to show the problem. = + + + + + + + +4 add 3 zero pairs subtract –3 Read and demonstrate the explanation with cubes. Demonstrate the solution of problems 10 and 13 with cubes in a jar. Sums and Differences: Dice Game This game may be used to practice computation with positive and negative numbers. Two colors of 6-sided dice are used, e.g., a green one for positive numbers and a red one for negative numbers. Players take turns throwing the two dice. The score for each throw is the algebraic sum of the positive and negative dots that are turned up. Play continues for a specified time. The winner is the player with the greatest absolute value, e.g., – 8 beats + 4. To practice subtraction, the dice can be thrown one at a time on a surface so that one lands on an area labeled minuend and the other on an area labeled subtrahend. Skill Builders p. 203 Lesson Plan Page 1 3 4 5 6 2 Program Overview ©MathTeachersPress, Reproduction by anymeans is stri Subtracting a number gives the same result as ad – 5 – 2 There are not any black cubes. Add 2 black and 2 white cubes so yo can subtract. Shortcut: Add the opposite of the number being s – 5 – 2 The opposite of 2 is – 2 Write the opposite of each number. 1. 7 _________ 5. 0 __________ 2. – 5 _________ 6. _________ 3. 2 7. – 9. 4 – ( – 2) __________ = ____ 12. – 4 – 6 __________ = ____ 15. – 6 – 6 __________ = ____ 18. – 3 – ( – 1) __________ = ____ 10. – 2 – 3 __________ = _ 13. 5 – ( – 1) __________ = _ 16. 5 – 0 __________ = _ 19. – 4 – ( – 5) __________ = _ Rewrite each subtraction problem as an additio 4 + 2 6 Which sentence is not true? A – 2 – ( – 7) = – 9 C 7 B – 2 – 6 = – 8 D 4 Adding Opposites: A Shortcut for Subtra -7 5 0 – 3 4 -10 -12 -2 -2 + -3 -4 + -6 5 + 1 -6 + -6 5 - 0 -3 + 1 -4 + 5 Objective: To subtract integers by adding the opposite. Materials: Black and white cubes (or positive and negative integer squares, Master 19), clear jar, 6-sided dice (two colors) Finding a Pattern In these activities students represent the minuend with black and white cubes in a clear jar and are then asked if there are enough integers to remove the subtrahend. When there are not enough integers to subtract, students will suggest that an equal number of black and white cubes may be added so there will be enough. Students will make a table showing each example and be guided to discover the pattern of adding the opposite as they discuss possible patterns in small groups. Write the following table on the board: ______________________________________________ Original Number No. being subtracted Difference ______________________________________________ 4 – 3 7 – 5 – 2 – 3 – 4 1 – 5 – 3 – 4 1 2 – 2 4 Divide the class into small groups. Give each group a set of black and white cubes to solve the problems. To find a pattern for subtracting integers, solve the problems with models and record the results in a table. Discuss the solutions in your group to see if you can find the pattern for subtracting integers. The pattern should be written in a complete sentence. To show 4 – ( – 3), place 4 black cubes in a jar. How can we remove three white cubes when there are none here? ( add 3 pairs of zero, i.e., 3 black cubes and 3 white cubes, to the jar) Record the difference of + 7. + 4 – ( – 3) = + 7 Pattern: To subtract integers, add the opposite of the number being subtracted. Alternatively, use positive and negative integer squares or write + and — signs to show the problem. = + + + + + + + +4 add 3 zero pairs subtract – 3 Read and demonstrate th cubes. Demonstrate the solu and 13 with cubes in a jar. Sums and D Dice Game This game practice comp and negative of 6-sided dice are used, e.g. positive numbers and a red numbers. Players take turns dice. The score for each thro sum of the positive and nega turned up. Play continues for a specif is the player with the greates – 8 beats + 4. To practice subtraction, th one at a time on a surface so area labeled minuend and t labeled subtrahend. Skill Builders p. 203 1 Before We Begin: Objective, Materials, Vocabulary Each lesson starts with a learning objective for the day, the materials required, and the math vocabulary word(s) introduced in the lesson. 2 Introductory Activities: Hands-On Learning The Introductory Activities section allows students to discover the day’s learning objective using an active, hands-on approach. The teacher will find a lightly scripted description of what to do, what to say, what questions to ask, and what answers to look for (with statements to be made aloud printed in bold type ). 3 About This Page: Student Practice The About This Page section links the hands-on activity to the pictures and practice on pages in the Student Book. Each Lesson Plan page number matches the corresponding page number in the Student Activity Book. 4 Follow-Up Activities: Closing the Lesson The Follow-Up Activities section provides additional instruc- tional support in the form of games, problem-solving activities, and suggested reinforcement Masters for remedial practice (found in the Skill Builders section of the Teacher Manual). 5 Games: As students discover the winning strategy for each game, they go throug steps similar to those used in problem solving. 6 Reinf rcement Masters: Many L sson Plan pages list a Skill Builders page to support the lesson and provide differentiat d instruc ion. These p ges may be used as homework or as additional in-class practice when needed.