Mathematics Standards Plus COMMON CORE INTERVENTION Grade 7 SAMPLER
Standards Plus COMMON CORE INTERVENTION Available for Grades 1-8 Language Arts and Math Standards Plus COMMON CORE INTERVENTION Mathematics Grade 7 A/B Topics: Ratios & Proportional Relationships The Number System Expressions & Equations TEACHER EDITION A/B Scaffolded lessons written to the Common Core Language Arts and Mathematics Standards. Includes: Pre- and Post- Assessments for each set of instruction on a topic or idea Step-by-step direct instruction lessons that support student mastery of grade level standards Performance Tasks that provide students opportunities to apply their learning 2 Great for: Small Group Instruction Summer School Programs After School Programs Special Ed - Academic IEP Goals
Standards Plus Common Core Intervention Mathematics Grade 7 Sampler Sampler Contents: Lesson Index... pgs 5-8 Sample Lessons...pgs 10-43 Expressions and Equations Pre Assessment 4 Lessons 12-23 Performance Task 4 Post Assessment 4 3
4 The lesson index on the next four pages lists every Mathematics Grade 7 lesson.
Ratios & Proportional Relationships Standards Plus Common Core Intervention Mathematics Grade 7 Domain Lesson Focus Standard(s) References TE pg St. Ed. pg DOK Pre 1 Pre- Assessment- Rate Problems & Percent 7.RP.1, 7.RP.2, 7.RP.3 14 A- 3 1 Ratio 16 A- 4 2 Unit Rate 18 A- 5 3 Rate 20 A- 6 4 Rate, Ratio, & Unit Rate 22 A- 7 5 Solving Rate Problems 24 A- 8 6 Average Speed Prerequisite skills and 26 A- 9 7 Rate & Average Speed scaffolded instruction to 28 A- 10 1-2 build readiness for grade 8 Solve for a Percent 30 A- 11 level standards and 9 Percent Discounted instruction. 32 A- 12 10 Sales Tax 34 A- 13 11 Fraction/Decimal Equivalents 36 A- 14 12 Percent as Fractions & Decimals 38 A- 15 13 Calculating Percent 40 A- 16 14 Calculating Percent 42 A- 17 P1 Performance Task #1 This Week s Specials (7.RP.1, 7.RP.2, 7.RP.3) 44 A- 18 3 Post 1 Post- Assessment- Rate Problems & Percent 7.RP.1, 7.RP.2, 7.RP.3 46 A- 19 1-2 The Number System Pre 2 Pre- Assessment- Integers & Absolute Value 7.NS.1, 7.NS.2, 7.NS.3 54 A- 21 1 Fractions & Mixed Numbers on a Number Line 56 A- 22 2 Decimals on a Number Line 58 A- 23 3 Using Number Lines 60 A- 24 4 Compare and Order Fractions & Decimals 62 A- 25 5 Compare and Order Fractions & Decimals 64 A- 26 6 Absolute Value 66 A- 27 Prerequisite skills and 7 Absolute Value 68 A- 28 scaffolded instruction to 1-2 8 Adding Integers build readiness for grade 70 A- 29 9 Adding Integers level standards and 72 A- 30 10 Subtracting Integers instruction. 74 A- 31 11 Subtracting Integers 76 A- 32 12 Multiplying Integers 78 A- 33 13 Multiplying Integers 80 A- 34 14 Dividing Integers 82 A- 35 15 Dividing Integers 84 A- 36 P2 Performance Task #2 Positive or Negative? (7.NS.2, 7.NS.3) 86 A- 37 3 Post 2 Post- Assessment- Integers & Absolute Value 7.NS.1, 7.NS.2, 7.NS.3 88 A- 38 1-2 5
Standards Plus Common Core Intervention Mathematics Grade 7 Domain Lesson Focus Standard(s) References TE pg St. Ed. pg DOK Pre 3 Pre- Assessment- Solving Equations 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4 96 B- 3 Expressions & Equations 1 Solving Equations with Variables 98 B- 4 2 Solving Equations with Variables 100 B- 5 3 Evaluating Variable Expressions 102 B- 6 4 5 6 7 8 Writing Variable Expressions Order of Operations Solving Addition & Subtraction Equations Solving Multiplication & Division Equations Solving Two- Step Equations Prerequisite skills and scaffolded instruction to build readiness for grade level standards and instruction. 104 106 108 110 112 B- 7 B- 8 B- 9 B- 10 B- 11 9 Solving Two- Step Equations 114 B- 12 10 Writing Equations 116 B- 13 11 Writing Equations 118 B- 14 P3 Performance Task #3 What Does It Mean? (7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4) 120 B- 15 3 Post 3 Post- Assessment- Solving Equations 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4 122 B- 16 1-2 Pre- Assessment- Solve/Graph Equations & Pre 4 Inequalities 12 Solve & Graph Linear Equations 7.EE.1, 7.EE.3, 7.EE.4 124 B- 17 126 B- 18 13 Solve Linear Equations 128 B- 19 14 Solve and Graph Linear Equations 130 B- 20 15 Solve and Graph Linear Equations 132 B- 21 16 Determining Slope Prerequisite skills and 134 B- 22 scaffolded instruction to 17 Determining Slope 136 B- 23 build readiness for grade 18 Inequalities 138 B- 24 level standards and 19 Solve Inequalities by Adding/Subtracting instruction. 140 B- 25 20 Solve Inequalities by Multiplying/Dividing 142 B- 26 21 Solve & Graph Inequalities 144 B- 27 22 Using Inverse Operations 146 B- 28 23 Using Inverse Operations 148 B- 29 P4 Performance Task #4 Word Problems with Inequalities (7.EE.3, 7.EE.4) 150 B- 30 3 Post- Assessment- Solve/Graph Equations & Post 4 7.EE.1, 7.EE.3, 7.EE.4 152 B- 31 1-2 Inequalities 1-2 1-2 Lessons provided as samples. See pages 10-43. 6
Standards Plus Common Core Intervention Mathematics Grade 7 Domain Lesson Focus Standard(s) References TE pg St. Ed. pg DOK Pre 5 Pre- Assessment- Data Displays 7.SP.4, 7.SP.8 16 C- 3 Statistics & Probability 1 Tree Diagrams 18 C- 4 2 Stem- and- Leaf Plots Prerequisite skills and 20 C- 5 scaffolded instruction to 3 Quartiles 22 C- 6 build readiness for grade 4 Quartiles 24 C- 7 level standards and 5 Box- and- Whiskers Plots instruction. 26 C- 8 6 Box- and- Whiskers Plots 28 C- 9 P5 Performance Task #5 Group Height Activity (7.SP.4, 7.SP.8) 30 C- 10 3 Post 5 Post- Assessment- Data Displays 7.SP.4, 7.SP.8 32 C- 11 1-2 Pre 6 Pre- Assessment- Probability 7.SP.1-7.SP.3, 7.SP.5-7.SP.7 34 C- 13 7 Certain, Likely, Unlikely, Improbable 36 C- 14 8 Probability 38 C- 15 9 Probability 40 C- 16 10 11 12 13 14 Samples of Populations Samples of Populations Predict Outcomes for a Simple Event Independent & Dependent Events Probability & Proportions Prerequisite skills and scaffolded instruction to build readiness for grade level standards and instruction. 42 44 46 48 50 C- 17 C- 18 C- 19 C- 20 C- 21 15 Calculate Probability for Compound Events 52 C- 22 16 Calculate Probability for Dependent Events 54 C- 23 17 Calculate Probability for Events 56 C- 24 P6 Performance Task #6 What Are the Chances? (7.SP.1-7.SP.3, 7.SP.5-7.SP.7) 58 C- 25 3 Post 6 Post- Assessment- Probability 7.SP.1-7.SP.3, 7.SP.5-7.SP.7 60 C- 26 1-2 1-2 1-2 7
Standards Plus Common Core Intervention Mathematics Grade 7 Domain Lesson Focus Standard(s) References TE pg St. Ed. pg DOK Pre 7 Pre- Assessment- Surface Area & Volume 7.G.3, 7.G.4, 7.G.6 68 D- 3 1 Determining Perimeter 70 D- 4 2 Determining Area 72 D- 5 3 Determining Area 74 D- 6 4 Determining Surface Area 76 D- 7 5 Determining Surface Area Prerequisite skills and 78 D- 8 scaffolded instruction to 6 Determining Surface Area 80 D- 9 build readiness for grade 7 Determining Surface Area 82 D- 10 level standards and 8 Determining Surface Area instruction. 84 D- 11 9 Determining Surface Area 86 D- 12 10 Determining Volume 88 D- 13 11 Determining Volume 90 D- 14 12 Determining Volume 92 D- 15 P7 Performance Task #7 What s the Difference? (7.G.3, 7.G.4, 7.G.6) 94 D- 16 3 Post 7 Post- Assessment- Surface Area & Volume 7.G.3, 7.G.4, 7.G.6 96 D- 17 1-2 1-2 Geometry Pre 8 Pre- Assessment- Circles 7.G.4 98 D- 19 13 Circles 100 D- 20 14 Circles Prerequisite skills and 102 D- 21 scaffolded instruction to 15 Circles 104 D- 22 build readiness for grade 16 Circles 106 D- 23 level standards and 17 Circles instruction. 108 D- 24 18 Circles 110 D- 25 P8 Performance Task #8 What Makes a Circle a Circle? (7.G.4) 113 NONE 3 Post 8 Post- Assessment- Circles 7.G.4 114 D- 26 1-2 1-2 Pre 9 Pre- Assessment- Angles & Triangles 7.G.2, 7.G.5 116 D- 27 19 Classifying Angles 118 D- 28 20 Classifying Angles 120 D- 29 21 Classifying Angles 122 D- 30 22 Classifying Angles Prerequisite skills and 124 D- 31 23 Classifying Angles scaffolded instruction to 126 D- 32 24 Classifying Angles build readiness for grade 128 D- 33 1-2 25 Classifying Triangles by Their Angles level standards and 130 D- 34 26 Classifying Triangles instruction. 132 D- 35 27 Classifying Triangles 134 D- 36 28 Determining Measures of Unknown Angles 136 D- 37 29 Determining Measures of Unknown Angles 138 D- 38 P9 Performance Task #9 Angle Map (7.G.2, 7.G.5) 140 D- 39 3 Post 9 Post- Assessment- Angles & Triangles 7.G.2, 7.G.5 142 D- 40 1-2 8
Turn the page to view a sample Pre-Assessment 9
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve/Graph Equations & Inequalities Pre Assessment: 4 Procedure: Each intervention assessment is designed to be completed independently by the students. Read the directions aloud, and ensure that students understand how to mark their answer choices. Review: Review the correct answers with students as soon as they are finished. St. Ed. pg. B-17 Answers: 1. m = 126 2. horizontal 3. p 10 4. w = 48 5. m 1 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 6. z > 7 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 10
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve/Graph Equations & Inequalities Pre Assessment: 4 Directions: Solve each problem. Write your answers on the lines. 1. Solve for m. 2m + 63 = 315 m = 2. What type of line has a slope of zero? 3. Simplify the inequality. p + 18 8 p 4. Solve for w. w = 8 6 5. Simplify and graph the following inequality on the number line below. m + 8 7 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 6. Simplify and graph the following inequality on the number line below. z 12 > 5 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 11
12 After each Pre-Assessment, a scaffolded set of stepby-step direct instruction lessons is provided. These lessons support student mastery of the assessed standards.
Turn the page to view the set of lessons that support Pre-Assessment 4. 13
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve & Graph Linear Equations Lesson: # 12 Lesson Objective: Solve and graph linear equations. Introduction: Students will use linear equations to complete x and y tables. Then, they will write the coordinate pairs defined in the tables. Finally, they will graph the line defined by the linear equation. Instruction: Today you will use linear equations to complete x and y tables. Here is an example of an x and y table and a linear equation. In this table, we see 6 in the x column. Next to the 6 is a 5 in the y column. Then, we have (5, 4), (4, 3), and (3, 2). The linear equation says, y = x 1. In each row, did they subtract 1 from x to find y? Yes. Guided Practice: Now, notice that the coordinate pairs are given. We will graph these coordinate pairs. Let s begin with (6, 5). The 6 is the x value, so we will move horizontally along the x axis to 6. Then, we ll move vertically up to 5. This is where we place the first point. Next, we will graph (5, 4). Let s move horizontally across to five, and vertically up to four. Draw the point. (Repeat with the remaining points.) Now, let s connect the points to make the line. Independent Practice: There are two more tables for you to try. Remember, You must use the linear equation to determine each missing value. Then, write the coordinate pairs and graph them on the coordinate plane. Review: After a few minutes, review together. St. Ed. pg. B-18 Closure: Today you determined the missing values in tables and wrote coordinate pairs to match the values using the given linear equations. Then, you graphed the linear equation. Answers: 1. (1, 2), (2, 4), (3, 6), and (4, 8); graphed line should begin at (1, 2) and extend up to the right to (4, 8). 2. (3, 2), (4, 3), (5, 4), and (6, 5); graphed line should begin at (3, 2) and extend up to the right to (6, 5). 14
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve & Graph Linear Equations Lesson: # 12 Examples: y = x 1 x y (6, 5) 6 5 (5, 4) 5 4 (4, 3) 4 3 (3, 2) 3 2 Directions: Use the linear equation to determine the missing values in each table. Then, write the coordinate pairs defined in the table, and graph them in the coordinate plane. 1. y = 2x x y Coordinate Pair 1 (1, ) 2 (2, ) 3 (3, ) 4 (4, ) 2. x = y + 1 x y Coordinate Pair 2 (, 2) 3 (, 3) 4 (, 4) 5 (, 5) 15
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Linear Equations Lesson: # 13 Lesson Objective: Identify, solve, and graph equations. Introduction: Students will read problems, complete tables, and write linear equations to explain situations. Instruction: Today you will read problems and create x and y tables to fit the problem situations. Then you will write the linear equation that fits each situation. Guided Practice: Let s look at the example. Vera has tomato plants in her garden. Each plant produces 12 tomatoes. Make a table to show the number of tomatoes (x) produced by 5, 10, 15, and 20 plants (y). Below this problem, we see a table that has been started for us. Look at the first row. When Vera has 5 plants, they produce 60 tomatoes. When she has 10 plants, how many tomatoes do they produce? (120) When she has 15 plants, how many tomatoes do they produce? (180) When she has 20 plants, how many tomatoes do they produce? (240) The linear equation is x = 12y. This means that to find x, we multiply y by 12. Independent Practice: Create a table and write the linear equation for each of the given situations. Review: After a few minutes, review together. Closure: Today you completed tables and wrote linear equations for problem situations. St. Ed. pg. B-19 Answers: 1. (125, 5); (250, 10); (375, 15); (500, 20); x = 25y 2. (17.65, 1); (35.3, 2); (88.25, 5); (176.5, 10); x = 17.65y 3. (5, 10); (12.5, 25); (25, 50); (50, 100); x =.5y 16
Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Linear Equations Lesson: # 13 Example: Vera has tomato plants in her garden. Each plant produces 12 tomatoes. Make a table to show the number of tomatoes (x) produced by 5, 10, 15, and 20 plants (y). x y 60 5 Linear Equation: 10 15 20 Student Page Directions: Create a table and write the linear equation for each of the given situations. 1. Vera s bean plants each produce 25 beans. Make a table to show the number of beans (x) produced by 5, 10, 15, and 20 plants (y). x y 125 5 10 15 Linear equation: 20 2. Vera buys fertilizer every month for her garden. It costs $17.65 a bag. Make a table to show what Vera pays (x) for 1, 2, 5, and 10 bags of fertilizer (y). x y 17.65 1 2 Linear equation: 5 10 3. Vera sells her tomatoes for $.50 each at the market. Make a table to show what Vera makes (x) for selling 10, 25, 50, and 100 tomatoes (y) at the market. x y 5 10 25 Linear equation: 50 100 17
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Linear Equations Lesson: # 14 Lesson Objective: Identify, solve, and graph linear equations. Introduction: Students will read problems, complete tables, and write and graph linear equations to explain situations. Instruction: Today you will read problems and create x and y tables to fit the problem situations. Then you will write the linear equation that fits the situations presented. Guided Practice: Let s look at the example. Vera has tomato plants in her garden. Each plant takes up 2 square feet in the garden. Make a table to show the number of square feet (x) required to grow 2, 5, 10, and 25 tomato plants (y). Write the linear equation. Then, graph the line on the coordinate grid. Below this problem, we see a table that has been started for us. Look at the first row. Two tomato plants take up 4 square feet. How many square feet would 5 tomato plants take up? (10) Ten tomato plants? (20) 25 tomato plants? (50) What is the linear equation for this table? (The linear equation is y = 2x.) This means that to find y, we multiply x by 2. Now, we need to graph the linear equation y = 2x. Let s graph each of the points: (2, 4), (5, 10), (10, 20), and (25, 50). Work together to graph the line on the coordinate plane. Independent Practice: Create a table and write and graph the linear equation for this word problem. Review: After a few minutes, review together. St. Ed. pg. B-20 Closure: Today you completed tables and wrote and graphed linear equations for problem situations. Answers: 1. (2, 3); (8, 12); (10, 15); (16, 24); x = 2 y; the four points should be 3 graphed on the coordinate grid and connected to form a line. 18
Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Linear Equations Lesson: # 14 Example: Vera has tomato plants in her garden. Each plant takes up 2 square feet in the garden. Make a table to show the number of square feet (x) required to grow 2, 5, 10, and 25 tomato plants (y). Write the linear equation. Then, graph the line on the coordinate grid. 60 Student Page x y 4 2 5 10 25 Linear Equation: 55 50 45 40 35 30 25 20 15 10 5 5 10 15 20 25 30 35 40 45 50 55 60 Directions: Create a table and write the linear equation for the given situation. Then, graph the line on the coordinate grid. 1. Vera sells her avocados at a price of 3 for $2 at the market. Make a table to show what Vera makes (x) for selling 3, 12, 15, and 24 tomatoes (y) at the market. x y 2 3 12 15 24 60 55 50 45 40 35 30 25 Linear Equation: 20 15 10 5 5 10 15 20 25 30 35 40 45 50 55 60 19
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Linear Equations Lesson: # 15 Lesson Objective: Identify, solve, and graph linear equations. Introduction: Students identify the linear equation expressed as a line in the coordinate grid. Instruction: Today you will look at lines that have been graphed on the coordinate grid. You will determine which linear equation is defined by each line. Guided Practice: Let s look at the example. Which equation defines line A on the coordinate grid below? Here we have three answer choices. We can write the coordinate pairs for several points on the line to help us determine the linear equation that is defined by the line. ( 9, 9), ( 8, 8), ( 7, 7), and ( 6, 6) are all points on this line. What is the relationship of x to y? (x is negative y) x = y. Do you see this equation as an answer choice? (Yes, C.) Circle answer choice C. Independent Practice: Determine the equation that defines the lines on the coordinate grid above. Review: After a few minutes, review together. St. Ed. pg. B-21 Closure: Today you identified the linear equation that matched a line graphed in the coordinate grid. Answers: 1. A 2. B 3. C 4. B 20
Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Linear Equations Lesson: # 15 Example: Which equation defines line A on the coordinate grid below? A. x = y 1 B. x = 1 y C. x = y C A 9 8 7 6 5 4 3 2 y 1 0 x 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 D 2 3 4 5 6 7 8 9 E B Student Page Directions: Determine the equation that defines the lines on the coordinate grid above. 1. Line B: A. x = y + 4 B. x = y 4 C. x = 4y 2. Line C: A. x = y + 9 B. x = y 9 C. x = 9y 3. Line D: A. x = y 1 B. x = y + 1 C. x = y 4. Line E: A. x = y B. x = y C. x = y 1 21
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Determining Slope Lesson: # 16 Lesson Objective: Interpret the slope of a line. Introduction: Today students will learn the meaning of slope and determine the slope of given lines. Instruction: One important property of straight lines is how they angle away from the horizontal. The x axis on the coordinate plane is a horizontal line. The slope of a horizontal line is zero. Vertical lines have no slope because they do not angle in a positive or negative direction from the horizon. All other lines have a slope that is positive or negative. To find the slope of a line, we must know the location of two points on the line. For this line, the two points are at (1, 2) and (5, 6). We use the y1 y2 formula m= to determine the slope of the line. The variable m represents the x x 1 2 slope. We see y 1 y 2. This means the y coordinate in the first coordinate pair minus the y coordinate in the second pair. We see x 1 x 2. This means the x coordinate in the first coordinate pair minus the x coordinate in the second pair. We divide to solve. Guided Practice: Let s find the slope for a line that has these two points: (1, 2) and (5, 6). We solve the problem like this: 2 6 4 m= = =1 1 5 4 What is the slope of a line that has these two points: (2, 6) and (5, 2)? We have 6 2 divided by 2 5, so we have 4 divided by 3. What is the slope? 4 3 St. Ed. pg. B-22 Independent Practice: Determine the slope of lines that contain the given points. Review: After a few minutes, review together. Closure: Today you determined the slope of lines. Remember, a horizontal line has a slope of zero, and a vertical line has no slope. Answers: 1. 1 2. 2 3. 1 4. 1 22
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Determining Slope Lesson: # 16 6 5 4 3 2 3 4 y 2 1 0 x 6 5 4 3 2 1 1 2 3 4 5 6 1 Slope formula: y1 y2 m= x x 1 2 (1, 2) and (5, 6) 2 6 4 m= = =1 1 5 4 5 6 Example: (2, 6) and (5, 2) Directions: Determine the slope of lines that contain the given points. 1. ( 6, 2) and ( 2, 2) 2. ( 5, 4) and ( 2, 2) 3. (2, 5) and (5, 2) 4. (6, 4) and (0, 2) 23
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Determining Slope Lesson: # 17 Lesson Objective: Interpret the slope of a line. Introduction: Today students will learn the meaning of slope and determine the slope of given lines. Instruction: One important property of straight lines is how they angle away from the horizontal. The x axis on the coordinate plane is a horizontal line. The slope of a horizontal line is zero. Vertical lines have no slope because they do not angle in a positive or negative direction from the horizon. All other lines have a slope that is positive or negative. To find the slope of a line, we need to know the location of two points on the line. The points of this line are (1, 2) and (5, 6). We use the formula y1 y2 m= to determine the slope of the line. The variable m represents the slope. We x x 1 2 see y 1 y 2. This means the y coordinate in the first coordinate pair minus the y coordinate in the second pair. We see x 1 x 2. This means the x coordinate in the first coordinate pair minus the x coordinate in the second pair. We divide to solve. Guided Practice: Let s find the slope for a line that has these two points: (1, 2) and (5, 6). We solve the problem like this: 2 6 4 m= = =1 1 5 4 What is the slope of a line that has these two points: (2, 8) and (9, 7)? We have 8 7 divided by 2 9, so we have 1 divided by 7. What is the slope? Independent Practice: Determine the slope of lines that contain the given points. Review: After a few minutes, review together. Closure: Today you determined the slope of lines. Remember, a horizontal line has a slope of zero, and a vertical line has no slope. 1 7 St. Ed. pg. B-23 Answers: 1. 2. 3. 4. 2 5 7 5 10 3 4 1 or 6 3 24
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Determining Slope Lesson: # 17 6 5 4 3 2 3 4 y 2 1 0 x 6 5 4 3 2 1 1 2 3 4 5 6 1 Slope formula: y1 y2 m= x x 1 2 (1, 2) and (5, 6) 2 6 4 m= = =1 1 5 4 5 6 Example: (2, 8) and (9, 7) Directions: Determine the slope of lines that contain the given points. 1. ( 2, 8) and ( 7, 6) 2. ( 6, 2) and ( 1, 9) 3. (5, 4) and (2, 6) 4. (9, 4) and (3, 8) 25
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Inequalities Lesson: # 18 Lesson Objective: Identify, solve, and graph inequalities. Introduction: Students will write inequalities today. Instruction: Today you will write inequalities. When we write equations, we use an equal sign because what comes on the left of equation is equal to what comes on the right of an equation. When we write inequalities, we use the less than, less than or equal to, greater than, or greater than or equal to symbols because the two sides are not equal. Look at you paper. Here are the four symbols we use when writing inequalities. (Point out the four symbols at the top of the page.) Here is an example of an inequality: a number 7 is less than 22. n 7 < 22. Guided Practice: Let s look at the example. A number +5 is greater than 12. We will use n as the variable, so let s write n. Then it says + 5. Let s write + 5. It says is greater than. What symbol do we use? (>) We write the greater than symbol. Finally, it says 12. Our inequality should read n + 5 > 12. Make sure you have written the inequality correctly on your paper. Independent Practice: There are six problems for you today. Remember, use the less than, less than or equal to, greater than, or greater than or equal to symbols to write the inequalities. Review: After a few minutes, review together. Closure: Today you wrote inequalities from given situations. Answers: 1. 3n 17 2. n 74 > 6 3. 2.17.002 +n 4. 43 < 54 +n 5. 9,435 > n 2 6. 12.54 4n St. Ed. pg. B-24 26
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Inequalities Lesson: # 18 < > Less than Less than or equal to Greater than Greater than or equal to A number 7 is less than 22. Example: A number + 5 is greater than 12. n 7 < 22 Directions: Read each situation. Write an inequality that matches each situation. Use the symbols above to show the correct comparison. 1. A number times 3 is less than or equal to 17. 2. 74 is greater than a number divided by 6. 3. 2.17 is greater than or equal to.002 + a number. 4. 43 is less than 54 + a number. 5. 9,435 is greater than a number 2. 6. 12.54 is less than or equal to 4 times a number. 27
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Inequalities by Adding/Subtracting Lesson: # 19 Lesson Objective: Identify, solve, and graph inequalities. Introduction: Students will write and solve inequalities to fit given situations today. Instruction: Today you will write and solve inequalities. When we write equations, we use an equal sign because what comes on the left of equation is equal to what comes on the right of an equation. When we write inequalities, we use the less than, less than or equal to, greater than, or greater than or equal to symbols because the two sides are not equal. Look at you paper. Here are the four symbols we use when writing inequalities. (Point out the four symbols at the top of the page.) Here is an example of an inequality: a number + 14 is less than or equal to 6. n + 14 6. When we solve inequalities, we isolate the variable. In this example, we isolate the variable by subtracting 14 from both sides: n 14 + 14 6 14. n 8. So, in this situation n is less than or equal to 8. Guided Practice: Let s look at the example. A number + 43 is greater than 9. We will use n as the variable, so let s write n. Then, it says + 43. Let s write + 43. It says is greater than. What symbol do we use? (>) We write the greater than symbol. Finally it says 9. Our inequality should read n + 43 > 9. Now we solve by subtracting 43 from both sides to isolate the variable. Now we have n + 43 43 > 9 43. We simplify: n > 52. Independent Practice: There are four inequalities for you to write and solve in today s lesson. Remember, use the less than, less than or equal to, greater than, or greater than or equal to symbols to write the inequalities. Review: After a few minutes, review together. Closure: Today you wrote and solved inequalities from given situations. Answers: 1. 83 n < 2; n < 81 2. 6.24 n + 1.4; 4.84 n 3. n 7 > 92; n > 85 4. 16.37 + n; 63 n St. Ed. pg. B-25 28
Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Inequalities by Adding/Subtracting Lesson: # 19 < > Less than Less than or equal to Greater than Greater than or equal to A number + 14 is less than or equal to 6. n + 14 6 n 14 + 14 6 14 n 8 Student Page Example: A number + 43 is greater than 9. Directions: Read each situation. Write and solve an inequality that matches each situation. Use the symbols above to show the correct comparison. 1. 83 a number is less than 2. 2. 6.24 is greater than or equal to a number + 1.4. 3. A negative number 7 is greater than 92. 4. 16 is less than or equal to.37 + a number. 29
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Inequalities by Multiplying/Dividing Lesson: # 20 Lesson Objective: Identify, solve, and graph inequalities. Introduction: Students will write and solve inequalities to fit given situations today. Instruction: Today you will write and solve inequalities. When we write equations, we use an equal sign because what comes on the left of equation is equal to what comes on the right of an equation. When we write inequalities, we use the less than, less than or equal to, greater than, or greater than or equal to symbols because the two sides are not equal. Look at you paper. Here are the four symbols we use when writing inequalities. (Point out the four symbols at the top of the page.) Here is an example of an inequality: a number 9 is greater than 27. n 9 > 27. When we solve inequalities, we isolate the variable. In this example, we isolate the variable by dividing both sides by 9: n 9 9 > 27 9. n > 3. So, in this situation n is greater than 3. Guided Practice: Let s look at the example: A number 22 is less than or equal to 34. We will use n as the variable, so let s write n. Then it says 22. Let s write 22. It says is less than or equal to. What symbol do we use? ( ) We write the less than or equal to symbol. Finally it says 34. Our inequality should read n 22 34. Now we solve by multiplying both sides by 22 to isolate the variable. Now we have n 22 22 34 22. We simplify: n 748. Independent Practice: There are four inequalities for you to write and solve in today s lesson. Remember, use the less than, less than or equal to, greater than, or greater than or equal to symbols to write the inequalities. Review: After a few minutes, review together. Closure: Today you wrote and solved inequalities from given situations. Answers: 1. 13n < 195; n < 15 2. 147 > n 3 ; 441 > n 3. 74 n 37; 2 n 4. 46n 874; n 19 St. Ed. pg. B-26 30
Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve Inequalities by Multiplying/Dividing Lesson: # 20 < > Less than Less than or equal to Greater than Greater than or equal to A number 9 is greater than 27. n 9 > 27 n 9 9 > 27 9 n > 3 Student Page Example: A number 22 is less than or equal to 34. Directions: Read each situation. Write and solve an inequality that matches each situation. Use the symbols above to show the correct comparison. 1. A number 13 is less than 195. 2. 147 is greater than a number 3. 3. 74 a number is greater than or equal to 37. 4. 46 a number is less than or equal to 874. 31
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Inequalities Lesson: # 21 Lesson Objective: Demonstrate an ability to write, solve, and graph inequalities. Introduction: Students will solve and graph inequalities in today s lesson. Instruction: Today you will solve and graph inequalities. When we solve equations, we end up with a line, but when we solve an inequality, there are many possible answers. We will learn how to show the possible answers in today s lesson. When we graph the inequalities, we will use a number line. It is important that you carefully note if the inequality symbol is greater than or less than OR greater than or equal to or less than or equal to. When we say 7 > n, 7 is not a possible answer. When we say 7 n, 7 is a possible answer. Guided Practice: Let s look at the example. 3 > n 4. We must multiply both sides by 4 to isolate the variable. 3 4 > n 4 4. 12 > n. Look at the number line. We must graph 12 > n. We do so by showing an open starting place at 12. Then, we darken the number line to the left of 12. This is to show than any number smaller than 12 correctly answers the inequality. If the inequality had been greater than or equal to, we would have darkened the starting place at 12 to include it as a possible answer. Independent Practice: There are four inequalities for you to solve in today s lesson. Solve each inequality and graph it on the number line. Review: After a few minutes, review together. Closure: Today you solved and graphed inequalities. St. Ed. pg. B-27 Answers: 1. n 10; 10 2. 22 n; 22 3. n < 40; 4. 10 > n; 40 10 32
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Solve and Graph Inequalities Lesson: # 21 Example: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 3 > n 4 3 4 > n 4 4 12 > n Directions: Solve and graph each inequality. 1. n 2 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 2. 550 n 25 0 2 4 6 8 10 12 14 16 18 20 22 24 26 3. n + 30 < 10 60 50 40 30 20 10 0 10 20 30 40 50 60 70 4. 14 > n 4 30 25 20 15 10 5 0 5 10 15 20 25 30 35 33
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Using Inverse Operations Lesson: # 22 Lesson Objective: Use inverse operations to solve problems. Introduction: Students will use inverse operations to solve problems in today s lesson. Instruction: An equation is a mathematical sentence with an equal sign. In an equation such as m + 5 = 27, a value of the variable that makes the equation true is called a solution. We can use inverse (opposite) operations to solve for the variable. We can solve equations using inverse operations. To solve or undo an addition equation, we will use subtraction. To solve or undo a subtraction equation, we will use addition. Guided Practice: Let s solve the examples together. Example A says m + 5 = 27. We isolate the variable by subtracting 5 from both sides of the equation: m + 5 5 = 27 5. We simplify, so m = 22. We check by substituting the solution for the variable: 22 + 5 = 27. Example B says k 3.6 = 4.2. We isolate the variable by adding 3.6 to both sides of the equation: k 3.6 + 3.6 = 4.2 + 3.6. We simplify, so k = 7.8. We check by substituting the solution for the variable: 7.8 3.6 = 4.2. Independent Practice: Use inverse operations to solve each problem. Review: After a few minutes, review together. Closure: Today you used inverse operations to solve problems. Answers: 1. 31 2. 59 3. 118 4. 41.92 5. 82.2 St. Ed. pg. B-28 34
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Using Inverse Operations Lesson: # 22 Example A: m + 5 = 27 Example B: k 3.6 = 4.2 Directions: Use inverse operations to solve each problem. 1. v 8 = 23 2. k + 13 = 72 3. r 18 = 100 4. m + 6.32 = 48.24 5. t 17 = 65.2 35
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Using Inverse Operations Lesson: # 23 Lesson Objective: Use inverse operations to solve problems. Introduction: Students will use inverse operations to solve problems in today s lesson. Instruction: An equation is a mathematical sentence with an equal sign. In an equation such as 3n=27, a value of the variable that makes the equation true is called a solution. We can use inverse (opposite) operations to solve for the variable. We can solve equations using inverse operations. To solve or undo a multiplication equation, we will use division. To solve or undo a division equation, we will use multiplication. Guided Practice: Let s solve the examples together. Example A is 6m = 42. We divide both sides of the equation by six to isolate the variable: 6m 6 = 42 6. We simplify, so m = 7. We check by substituting the solution for the variable: 6 7 = 42. Example B is 7 r = 6. We multiply both sides of the equation to isolate the variable: 7 r 7 = 6 7. We simplify, so r = 42. We check by substituting the solution for the variable: 42 7 = 6. Independent Practice: Use inverse operations to solve each problem. Review: After a few minutes, review together. Closure: Today you used inverse operations to solve problems. Answers: 1. 176 2. 20.2 3. 120 4. 1.4 St. Ed. pg. B-29 36
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Domain: Expressions & Equations Focus: Using Inverse Operations Lesson: # 23 An equation is a mathematical sentence with an equal sign. In an equation such as 3n=27, a value of the variable that makes the equation true is called a solution. We can use inverse (opposite) operations to solve for the variable. To solve or undo a multiplication equation, we use division. To solve or undo a division equation, we use multiplication. Example A: 6m = 42 Example B: 7 r = 6 Directions: Use inverse operations to solve each problem. 1. m = 8 22 3. z 2.5 = 48 2. 3r = 60.6 4. 1.2y = 1.68 37
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Teacher Lesson Plan St. Ed. pg. B-30 Standards Plus Common Core Intervention Mathematics Grade 7 Expressions & Equations Performance Task #4 Lesson Objective: The students will write word problems to match given inequalities. Instruction: Review the information at the top of the student page. Guided Practice: Present the inequality K 2. Have the students work in groups of 3 4 to write a word problem that would be simplified using the given inequality. Have groups share their word problems. Independent Practice: Have the students work individually to write word problems to match the inequalities found at the bottom of the student page. Review: Have students present their word problems to the group they worked with during Guided Practice. Debrief as a whole class. 40
Student Page Standards Plus Common Core Intervention Mathematics Grade 7 Expressions & Equations Performance Task #4 < > Less than Less than or equal to Greater than Greater than or equal to, Graph has a filled in endpoint. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 <, > Graph has an open endpoint. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 Example: K 2 Directions: Write a word problem that would be solved using each of the following inequalities. 1. 7 < g 2. c 9 3. y > 4 41
Teacher Lesson Plan Standards Plus Common Core Intervention Mathematics Grade 6 Domain: Ratios & Proportional Relationships Focus: Rates & Proportions Post Assessment: 4 Procedure: Each intervention assessment is designed to be completed independently by the students. Read the directions aloud, and ensure that students understand how to mark their answer choices. Review: Review the correct answers with students as soon as they are finished. St. Ed. pg. B-31 Answers: 1. 30 miles/gallon 2. 1,020 minutes 3. $800 4. $31.00 5. m = 2 6. The 24 donut box is less expensive than two 12 donut boxes. A Post-Assessment is also provided to show evidence of student growth. 42
Student Page Standards Plus Common Core Intervention Mathematics Grade 6 Domain: Ratios & Proportional Relationships Focus: Rates & Proportions Post Assessment: 4 Directions: Solve each problem. Write your answers on the lines. 1. Tom s car traveled 600 miles using 20 gallons of gas. How many miles did Tom get per gallon? Find the unit rate and write in lowest terms. 2. How many minutes in 17 hours? 3. Shawna saves $40 out of every $80 she earns. How much will she need to earn to save $400 she needs for her vacation? 4. Steve did 4 hours of yard work and was paid $7.75 an hour. How much money did he make? 5. Solve for m. 15 30 = m 4 Directions: Solve the problem below. Write your answer on the line below. 6. You can buy Delicious Donuts in two different size boxes. You can buy a one dozen box for $6.58, or you can buy a 24 donut box for $12.70. Which is the better buy? 43
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