Summer Math. AchieveMath. Level # Lesson 00Teacher Lesson Manual SAMPLE. Intensive. Catapult Learning Catapult Learning

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1 Summer Math Intensive L.8 AchieveMath Level # Lesson 00Teacher Lesson Manual Catapult Learning SAMPLE 2013 Catapult Learning

2 Math At-A-Glance Teacher Sheet 10 Problem Solving Strategies Act Out or Use Objects Make a Picture or Design Use or Make a Table Make an Organized List Guess and Check Look for a Pattern Work Backwards Use Logical Reasoning Make it Simpler Brainstorm Questioning Evaluation judge, justify, interpret, conclude, infer, assess Synthesis combine, develop, organize, revise, cause/effect, generate Analysis analyze, differentiate, compare, contrast, diagram Application demonstrate, apply, use Comprehension restate, explain, locate Knowledge define, recall, list, name Wait Time STUDENTS should be given wait time of 10 seconds to answer a question. ALLOW the student you originally called on, ample opportunity to respond CONSISTENCY is the key to establishing questioning protocols REPHRASE, REDIRECT, or MAKE SIMPLER if the student does not respond, or responds incorrectly. Open-Ended Questions for Math How did you do that? What should you do now? What do you think? What do you see? Is there another way to do it? What is a good guess? Wait time has been shown to increase: participation, thoughtful response, self-esteem, and on-task behavior. What do you estimate?

3 SEQUENCE OF MATH LEARNING OBJECTIVES - LEVEL 8 SKILLS NCTM #Lessons WP 8.1A Order integers X 1 WP A Add integers, like and unlike signs X 2 WP A Subtract integers, like and unlike signs X 2 WP A Add three one-digit integers X 2 WP A Multiply integers, like and unlike signs X 2 WP A Divide integers, like and unlike signs X 1 WP A Use operational orders, shown by parentheses X 3 WP A Write exponent as a multiplication expression X 2 WP A Use order of operations X 1 WP A Identify the smallest/largest fraction X 1 WP A Add and subtract fractions with unlike denominators X 2 WP A Multiply a whole number by a fraction X 1 WP A Identify the reciprocal of a fraction X 1 WP A Multiply and divide fractions X 2 WP A Divide a whole number by a fraction X 1 WP A Identify equivalent decimal for a fraction X 1 WP A Write a decimal in expanded notation X 1 WP A Add decimal fractions, convert to decimal number X 1 WP A Multiply decimals, two/three decimal digits X 2 WP A Divide a decimal by a whole number, three decimal digits X 1 WP 8.3

4 SKILLS NCTM #Lessons WP 8.21A Divide decimals, one decimal digit divisor X 1 WP A Find the percent of a number, including money notation X 3 WP A Identify proportions in a ratio X 1 WP A Understand four coordinate graph X 2 WP A Evaluate a two variable algebraic equation X 2 WP A Calculate the perimeter of squares, rectangles, triangles, and irregular polygons 8.27A Calculate the area of squares, rectangles, triangles, and irregular polygons 8.28A Calculate the volume of cylinders and triangular prisms X 2 WP 8.2 X 2 WP 8.3 X 2 WP A Identify the probability of an outcome X 2 WP A Interpret a Venn diagram X 1 WP 8.2 WORD PROBLEMS WP 8.1 Solve multi-step word problems using the four operations X 5 WP 8.2 Use a diagram to solve a word problem X 8 WP 8.3 Use proportion to solve a word problem X 4 WP 8.4 Use logical reasoning X 2 WP 8.5 Identify percentage in a word problem X 3 WP 8.6 Solve simple interest word problems X 4 WP 8.7 Solve unit price word problems X 4 DATA COLLECTION AND ANALYSIS DC 8.1 Use and compare data on a bar graph to solve problems DC 8.2 Analyze and interpret data plotted on a double line graph X 2 X 3 DC 8.3 Read a chart and identify missing information X Include in DC 8.1/8.2

5 SKILLS NCTM #Lessons WP AUTOMATIC OBJECTIVES HOS1 Develop higher order thinking skills HOS2 Develop ability to reason, communicate, connect and problem solve in math HOS3 Develop mental math strategies X X X Combine with WP/DC Combine with WP/DC Combine with WP/DC

6 Catapult AchieveMath Program Vocabulary List, Level 8 integers exponent percent least power proportion greatest base whole positive integers variable part negative integers multiple discount sum greater than ratio positive sign less than cross multiply negative sign equal graph subtract equivalent fraction coordinates difference least common ordered pairs factors denominator origin product improper fraction point divide mixed number quadrants divisor numerator equation dividend denominator evaluate quotient cancel perimeter operations greatest common factor square multiply reciprocal rectangle add whole numbers triangle operational order lowest terms polygon parentheses terminating irregular polygon data repeating area data collection necessary zero volume bar graph expanded form cylinder horizontal decimals radius vertical place value diameter Venn diagram tenths triangular prism x-axis hundredths probability y-axis thousandths outcomes data tables digits chances double line graph word problems event analyze rounding tree diagram

7 Catapult AchieveMath Materials Scope & Sequence Level 8. Lesson Materials Corresponding Vocabulary 1 Integer Number Lines (student worksheets), loose-leaf paper, pencils 2 Integer Number Lines (student worksheets), loose-leaf paper, pencils 3 Number Line (student worksheets), pencils, loose-leaf paper, dry erase boards/markers/erasers 4 Integer Number Lines (student worksheets), loose-leaf paper, dry erase boards/markers/erasers, pencils integers, whole numbers, least, greatest positive integers, negative integers, sum integer, positive sign, negative sign, sum subtract, difference, like signs, opposite 5 Integer Number Lines (student worksheets), two-color counters, pencils, loose-leaf paper subtract, difference, unlike signs 6 Two-color counters, pencils, loose-leaf paper positive integers, negative integers, sum 7 Two-color counters, pencils, loose-leaf paper positive sign, negative sign, sum 8 Pencils, loose-leaf paper factors, product, positive sign, negative sign 9 Pencils, loose-leaf paper factors, product, positive sign, negative sign, absolute value 10 Two-color counters, loose-leaf paper, pencils, dry erase boards/markers/erasers divide, quotient, negative integer, positive integer, absolute value 11 Pencils, loose-leaf paper operations, multiply, divide, add, subtract, operational order 12 Calculators, pencils, loose-leaf paper operational orders, parentheses 13 Calculators, loose-leaf paper, pencils operational orders, parentheses 14 Test Taking Strategies Level 8 8/2004

8 Catapult AchieveMath Materials Scope & Sequence Level Math Benchmark Assessment 16 Graph paper (1/4 inch grids, 2 sheets per student), 12- inch rulers, pencils, Used Numbers, Statistics: The Shape of the Data (Grades 4-6), pp , 78 (for reference), How Long Do People Sleep? Data sheet, (student worksheets) 17 Used Numbers, Statistics, Grades 4-6, pages 63-67, 78 (for reference), How Long Do People Sleep? Data sheet (student worksheets), Teacher s Copy of Sleep Data (double line graph), Two student drawn vertical graphs (from previous class), Graph paper (1/4 inch grids), 12- inch rulers, pencils, colored pencils, calculators 18 Base Ten Blocks, dry boards/markers/erasers, deck of cards (A-5 of one suit), pencils 19 Dry erase boards/markers/erasers, playing cards (ace through ten of one suit and all queens/kings/jacks), pencils 20 Order of operations terms (student worksheets), die, Independent Practice Worksheet (student worksheets), pencils, loose-leaf paper, dry erase marker boards/markers/erasers 21 fraction circles, dry erase boards/markers/erasers, pencils, loose-leaf paper 22 Independent Practice Worksheet (student worksheets), fraction tiles, dry erase boards/markers/erasers, pencils, 23 fraction tiles, dry erase boards/markers/erasers, pencils, loose-leaf paper data collection, bar graph, data, horizontal, vertical, y-axis, x-axis data tables, graphs, double line graph, analyze, x-axis, y-axis, key exponent (power), base, factor exponent (power), base, variable parentheses, exponents multiple, greater than, less than, equal, equivalent fraction, least common denominator (LCD) sum, least common denominator (LCD), mixed number, improper fraction difference, least common denominator, multiple Level 8 8/2004

9 Catapult AchieveMath Materials Scope & Sequence Level fraction tiles, dry erase boards/markers/erasers, pencils, deck of cards, dice, loose-leaf 25 Daily Tune-Ups, Grade 6, pg. 35, twelve dice, dry erase boards/markers/erasers, deck of cards (minus face cards), pencils, 26 dry erase boards/markers/erasers, pencils, graph paper, crayons, fraction circles, loose-leaf paper, rulers factor, product, cancel, numerator, denominator, improper fraction, mixed number, greatest common factor (GCF) reciprocal, numerator, denominator, improper fraction, mixed number, whole number numerator, denominator, product, lowest terms 27 dry erase boards/markers/erasers, pencils, graph paper, crayons, loose-leaf paper, rulers 28 dry erase boards/markers/erasers, pencils, fraction tiles, loose-leaf paper numerator, denominator, reciprocal, lowest terms, greatest common factor, cancellation reciprocal, numerator, denominator, whole, product 29 Test Taking Strategies 30 Math Benchmark Assessment Level 8 8/2004

10 Catapult Learning AchieveMath Group Skill Sheet Level 8 Level 8 TEACHER: SCHOOL YEAR: DAYS FOR INSTRUCTION: Directions: Record Daily Lesson Assessment percent and the MBA percent next to the specific lessons. If there is no score for a given lesson, insert a check if a student was in attendance and A if a student is absent when the lesson was taught. STUDENTS MATH SKILLS DATE * MBA 1 Pre-test 1 Order integers 2 Add integers, like and unlike signs 3 Add integers, like and unlike signs 4 Subtract integers, like and unlike signs 5 Subtract integers, like and unlike signs 6 Add three one-digit integers 7 Add three one-digit integers 8 Multiply integers, like and unlike signs 9 Multiply integers, like and unlike signs 10 Divide integers, like and unlike signs 11 Use operational orders, shown by parentheses 12 Use operational orders, shown by parentheses 13 Use operational orders, shown by parentheses 8/04

11 Level 8 MATH SKILLS DATE 14 Review Lesson/Test Strategies 15 MBA 1 Post-test 16 Data Collection Part 1 17 Data Collection Part 2 * MBA 2 Pre-test 18 Write exponent as a multiplication expression 19 Write exponent as a multiplication expression 20 Use order of operations with exponents 21 Identify the smallest or largest fraction 22 Add and subtract fractions with unlike denominators 23 Add and subtract fractions with unlike denominators 24 Multiplication a whole number by a fraction 25 Identify the reciprocal of a fraction 26 Multiply and divide fractions 27 Multiply and divide fractions 28 Divide a whole number by a fraction 29 Review Lesson/Test Strategies 30 MBA 2 Post-test * MBA 3 Pre-test 31 Identify equivalent decimal for a fraction 8/04

12 Level 8 MATH SKILLS DATE 32 Write a decimal in expanded notation 33 Add decimal fractions, convert to decimal number 34 Multiply decimals, two to three decimal digits 35 Multiply decimals, two to three decimal digits 36 Divide a decimal by a whole number, three decimal digits 37 Divide decimals, one decimal digit divisor 38 Find the percent of a number, including money notation 39 Find the percent of a number, including money notation 40 Find the percent of a number, including money notation 41 Identify proportions in a ratio 42 Understand four coordinate graphs 43 Understand four coordinate graphs 44 Review Lesson/Test Strategies 45 MBA 3 Post-test 46 Data Collection Part 1 47 Data Collection Part 2 * MBA 4 Pre-test 48 Evaluate a two variable algebraic equation 49 Evaluate a two variable algebraic equation 50 Calculate the perimeter of squares, rectangles, triangles, and irregular polygons 8/04

13 Level 8 MATH SKILLS DATE 51 Calculate the perimeter of squares, rectangles, triangles, and irregular polygons 52 Calculate the area of squares, rectangles, triangles, and irregular polygons 53 Calculate the area of squares, rectangles, triangles, and irregular polygons 54 Calculate the volume of cylinders and triangular prisms 55 Calculate the volume of cylinders and triangular prisms 56 Identify the probability of an outcome 57 Identify the probability of an outcome 58 Interpret a Venn Diagram 59 Review Lesson/Test Strategies 60 MBA 4 Post-test 8/04

14 Catapult Learning AchieveMath Program Sequence of Lessons Orientation Lesson MBA 3 Pre-test, Lesson 31 Assessment of Student Achievement Lesson 32 MBA 1 Pre-test, Lesson 1 Lesson 33 Lesson 2 Lesson 34 Lesson 3 Lesson 35 Lesson 4 Lesson 36 Lesson 5 Lesson 37 Lesson 6 Lesson 38 Lesson 7 Lesson 39 Lesson 8 Lesson 40 Lesson 9 Lesson 41 Lesson 10 Lesson 42 Lesson 11 Lesson 43 Lesson 12 Lesson 44 Review/Test Strategies Lesson 13 Lesson 45 MBA 3 Post-test Lesson 14 Review/Test Strategies Lesson 46 Data Collection/Analysis Lesson 15 MBA 1 Post-test Lesson 47 Data Collection/Analysis Lesson 16 Data Collection/Analysis MBA 4 Pre-test, Lesson 48 Lesson 17 Data Collection/Analysis Lesson 49 MBA 2 Pre-test, Lesson 18 Lesson 50 Lesson 19 Lesson 51 Lesson 20 Lesson 52 Lesson 21 Lesson 53 Lesson 22 Lesson 54 Lesson 23 Lesson 55 Lesson 24 Lesson 56 Lesson 25 Lesson 57 Lesson 26 Lesson 58 Lesson 27 Lesson 59 Review/Test Strategies Lesson 28 Lesson 60 MBA 4 Post-test Lesson 29 Review/Test Strategies Assessment of Student Achievement Lesson 30 MBA 2 Post-test

15 Orientation Lesson - Math The Orientation Lesson will be delivered during the first session. The purpose of this lesson is: to help students become familiar with the goals and expectations of the program; to orient students to the components of the instructional sessions; to familiarize students with materials they will use throughout the course; and to introduce students to the motivation program. To help you with the orientation lesson, the following materials are needed: Teacher Materials: Math Lessons Binder Manipulatives and Teacher Resources Dry-erase board, marker, and eraser Tokens Student Materials: Student portfolio (two pocket folder) Dry-erase boards, markers, and erasers Pencils and loose-leaf paper Token cups The following topics comprise the Orientation Lesson: Welcome Welcome students warmly by name and introduce yourself to the group. Lead the students in a discussion of why they are there. Ask the following questions: o How many of you like sports or music? o What are your favorites? o How do we become better at sports or music? (by practicing, taking classes, modeling others) o Who helps you practice? (a coach, a friend, a parent, brother, a sister, a teacher) We are going to do the same thing here with math. We are going to get better at math and help make math fun by coaching you and helping you practice. Explain to students that they will be coming to sessions times each week. Explain that their attendance is important and that just as a coach wants you at practice and to attend all of the games, it is important that they attend each and every session to build their math skills. Inform students of the schedule for the class. Encourage students to be on time. Lead the students in a discussion of Why it is important to be on time

16 INTRODUCTION TO PROGRAM MATERIALS AND COMPONENTS Motivation Program Introduce students to the motivation program. Explain the components of the motivation program (praise, tokens, Token Tracker, Awards Center, certificates); draw a hand on the dry-erase board and label each digit with each of the components to help illustrate each component of the program. Direct students to turn to the Token Tracker in their student portfolio and to write their name on the top of the page. Review the components of the page and the procedures for entering information on the page. Tell students they will earn 5 tokens for attending today, and 10 tokens for completing the ASA. Direct them to enter today s token information on the first line of their Token Tracker. Discuss with students how they will be receiving specific feedback regarding their performance during their time in the program. Direct students to turn in their student portfolio to the page titled, How Do I Earn Tokens? Reinforce with students that: o they will earn tokens for attendance, attitude, achievement, and effort. o when they earn their tokens, they should leave them in the cup in which they are placed and wait until the end of the session to count them. o they will count and deposit their tokens by filling out the Token Tracker. The teacher will recount the tokens and verify the balance and initial it in pen. The teacher will also reclaim the tokens deposited. o tokens can be redeemed at the Awards Center on designated days which occur times per month. If possible, show students some items from the Awards Center so they have an idea of what they might be able to earn. Inform students that they do not have to get an item each time the Awards Center is open. They may save their tokens and redeem them at a future date. Discuss with students that the tokens they earn are theirs and should not be shared with others. Preview of Manipulatives Introduce students to math manipulatives for their level by laying some out on the instructional table. Ask students how they show respect for materials. Allow students a few minutes to explore with the manipulatives. Tell students that their pencils should be kept in their token cup whenever they are not using them (this will avoid pencil tapping, breaking pencils, etc.). Student Portfolio Explain to the students that they will each have their own student portfolio (a twopocket folder), which will remain at the site when they leave each day. Direct the students to write their names on the cover of their portfolio.

17 Explain that each student will have a packet of lesson worksheets to be inserted into their portfolios. Explain that all work will either be done on these worksheets or on loose-leaf paper. Dry-erase boards (review and demo with elementary school students only) Provide each student with a dry-erase board, marker, and eraser. Inform students that they will be using their dry-erase boards at various times throughout their sessions as part of their learning and practice activities. Allow students a few minutes to practice writing on the boards, by writing their names, a favorite color, sport, or activity. Problem Solving Strategies Engage students in a discussion of strategies they use when they come across word problems. Review student responses. Direct students to refer to the page in their student portfolio titled Math Student At-A-Glance Sheet. Lead the students in a discussion and a review of each component. Summary/Closure Inform students that at the end of each session they will be asked to share what they learned. Lead students in a discussion of what was learned during today s orientation session (schedule, motivation program, Awards Center). Inform students that after discussing what they learned they will be asked to count their tokens and enter the total on their Token Tracker. Follow these procedures to have students count and record their token totals for the session. NOTE: Students should leave the Orientation Lesson feeling excited about the program and about returning for their next session. Remember to address students by name as they leave and send them off on a positive note.

18 Lesson 1 DIRECTED MATH ACTIVITY L8, Lesson 1 Lesson Objective Order integers from the least to the greatest Word Problem Objective Solve simple interest word problems Materials/Manipulatives Integer Number Lines (student worksheets), loose-leaf paper, pencils Welcome (3 min.) Brief Review and Practice (10 min.) Skill: Ordering numbers Say: Who can tell me the difference between greatest and least? (Greatest means the largest or the most; least means the smallest or the fewest.) Say: Let s review placing numbers in order from the least to the greatest. If I give you three numbers, 5, 6, and 7, what number is greatest and what number is least? (7 is the greatest and 5 is the least) Place these numbers in order from the least to the greatest: 12, 21, 4, 11. (4,11,12, 21) Teacher: Write three more problems on the board and have students place numbers in order from least to greatest. 1.) 304, 367, 321, 375 (304, 321, 367, 375) 2.) 257, 48, 27, 66 (27, 48, 66, 257,) 3.) 99, 89, 101, 110, 91 (89, 91, 99, 101, 110) 4 AM8 Lesson 1

19 Lesson 1 Word Problem Say: We will work on a word problem together. Listen as I read the problem. Mrs. Simpson deposited $500 into a savings account that pays 5% interest per year. How much interest did Mrs. Simpson earn in one year? Say: What formula do we need to know in order to determine how much interest Mrs. Simpson earns? (interest = principal x rate x time) What is the principal amount in this problem? (the amount of money that she has in her account, $500) What is the rate? (the percent, 5%. For the problem we need to change it to a decimal, 0.05) What is the time? (she receives interest in a year) Teacher: Set up the problem on the board. Interest = principal x rate x time = $500 x 0.05 x 1 = $25.00 Mrs. Simpson receives $25.00 in interest in one year. Corresponding Vocabulary Teacher: Write the following vocabulary words on a board. Discuss these words and their meanings throughout the lesson. Integers, whole numbers, least, greatest Concept Development (10 min.) Say: Today, we are going to learn about integers. An integer is a whole number. What is a whole number? (A number that does not contain a portion, fraction, or decimal.) An example of a whole number is the number 5. 5½ or 5.6 are not whole numbers. Integers are actually whole numbers that can be positive or negative. If I have two dollars in my pocket, that is + 2. If I do not have any money in my pocket and I owe someone two dollars, then I have 2. Teacher: Draw an integer number line on the board. Point out the zero. Show the students how negative integers are to the left of the zero and positive integers are to the right of the zero AM8 Lesson Catapult Learning 5

20 Lesson 1 Say: Where is 5 located? (to the left of zero by five spaces) Where is + 6 located? (to the right of zero by six spaces) Where is 13 located? (to the left of zero by thirteen spaces) Guided Practice (15 min.) Teacher: Have students find the Integer Number Lines sheet in their portfolios. Students will also need paper. Students will work in two groups. Draw a number line on the board and demonstrate with your finger where 0, + 3, and 3 are located. Say: Let s break into two groups. You will use your Integer Number Lines. First, place your finger on zero. Next, place your finger on + 3. Now, place your finger on 3. Teacher: As each integer below is mentioned, monitor students to ensure they are pointing to the proper place on the number line. Say: I am going to give you three numbers. Place your fingers on the three numbers on the first number line on your page. The three integers are: - 4, + 2, and, - 1. Say: Remember that integers to the left of zero on the number line are negative. In other words, left is least. Integers to the right of zero on the number line are positive. In other words, right means greatest. Teacher: Write the following problems on the board. Have the students work in pairs to solve these problems. Say: Here are five problems. Use the number lines and work with a partner to solve each problem. Arrange the numbers in order from least to greatest. Write your answers on your paper , - 2, - 6 ( - 6, - 2, + 3) 2. 8, + 8, - 4 ( - 8, - 4, + 8) , - 1, 0, + 3 ( - 1, 0, + 1, + 3) 4. 6, - 10, - 8 ( - 10, - 8, - 6) , - 5, + 9, - 4 ( - 5, - 4, + 4, + 9) Teacher: Review the correct answers with the students. 6 AM8 Lesson 1

21 Lesson 1 Independent Practice/Application (7 min.) Say: Let s work on some practice problems. Copy the problems from the board onto your paper and then solve. Remember, we are putting these integers in order from the least to the greatest. Teacher: Write the following problems on the board. Students should complete their work independently. Review the correct answers with the students , 0, - 7 ( - 7, 0, + 3) , - 10, - 5 ( - 10, - 5, + 4) 3. 6, - 9, - 3 ( - 9, - 6, - 3) 4. 8, + 6, 0, + 2 ( - 8, 0, + 2, + 6) , - 1, 0, - 2 ( - 2, - 1, 0, + 1) , - 4, + 2, - 3 ( - 4, - 3, + 2, + 5) 7. 4, - 2, - 1, + 5 ( - 4, - 2, - 1, + 5) , - 9, - 14, + 8 ( - 14, - 9, + 8, + 13) , + 5, 0, - 7, - 17 (- 17, - 7, 0, + 5, + 9) 10. 8, - 4, + 1, - 11, + 5 (- 11, - 8, - 4, + 1, + 5) Closure (15 min.) Lesson Summary (1 minute) What did we do today? What is one thing you learned today? Administer Daily Lesson Assessment (8 minutes) Check all work. Score and record results on the Math Group Skills Sheet , - 2, + 4 ( - 2, + 3, + 4) 2. 6, - 3, + 5, 0 ( - 6, - 3, 0, + 5) , 0, - 9, + 5 ( - 9, 0, + 5, + 7) , - 4, - 10, + 2, - 8 ( - 10, - 8, - 4, + 2, + 6) 5. 0, + 2, + 8, - 5, - 7, - 1 ( - 7, - 5, - 1, 0, + 2, + 8) Tokens/Token Tracker/Awards Center (6 minutes) AM8 Lesson Catapult Learning 7

22 Lesson 1 Daily Lesson Assessment NAME DATE SKILL: Order integers from the least to the greatest. Write these integers in order from the least to the greatest: 1) + 3, - 2, + 4 2) - 6, - 3, + 5, 0 3) + 7, 0, - 9, + 5 4) + 6, - 4, - 10, + 2, - 8 5) 0, + 2, + 8, - 5, - 7, AM8 Lesson 1

23 Lesson 1 INTEGER NUMBER LINES AM8 Lesson Catapult Learning 9