Unit 2 (continued): Expressions and Equations 2 nd 9 Weeks Suggested Instructional Days: 10 Unit Summary (Learning Target/Goal): Use properties of operations to generate equivalent expressions. CCSS for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Unit Timeline Standards Learning Expectation & Vocabulary Resources Expression and Equations Use properties of operations to generate equivalent expressions. 3 7.EE.4b: Graph, write, and solve 1 day 7.EE.4b: Graph, write, and solve 2 7.EE.4b: Graph, write, and solve Graphing and writing inequalities. Solve and graph inequalities and make sense of the inequality in context. Inequalities may have negative coefficients. Problems can be used to find a maximum or minimum value when in context. As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions. Adding and subtracting inequalities h + 8 < -13 and b 4 > -6 Multiplying and dividing inequalities Write an inequality for each of the sentences: 12 is less than the product of -3 and a number; and the quotient of a number and 5 inequality; solution of an inequality; greater than; less than; greater than or equal; less than or equal; open circle; closed circle; compound inequality; addition and subtraction property of inequality; inverse operations division and multiplication property of inequality 3-1 3-2 3-3 7 th Grade Math Quarter 2 1
is at least -8. 2 7.EE.4b: Graph, write, and solve Solving 2 step inequalities Kate sells bracelets at a craft fair and earns $9.60 per bracelet. She pays a rental fee of $32.50 for her booth. She wants to earn at least $200. Write an inequality to find the number of bracelets Kate needs to sell. Graph and describe the solutions. 3-4 2 7.EE.4b: Graph, write, and solve Unit Review and Math 7 Q2 CFA #2 Discovery Education Assessment Unit 3: Ratios and Proportional Relationships 2 nd 9 Weeks Suggested Instructional Days: 28 Unit Summary (Learning Target/Goal): Analyze proportional relationships and use them to solve real-world and mathematical Writing ratios, equivalent ratios, comparing ratios ratios; equivalent ratios 4-1 Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical 1 day 2 A bag contains colored marbles. The ratios of red marbles to blue marbles is 1:4. The ratios of blue marbles to yellow marbles is 2:5. What is the ratio of red marbles to yellow marbles? Unit rates and proportional reasoning Find the unit rate: 2.4 miles in 11.5 minutes rate; unit rate; unit cost 4-2 Proportional Reasoning Unit http://schools.nyc.gov/nr/r donlyres/41c0f04c- 0BD6-491F-9BF0-16485EC080BE/0/NYCD OEG7MathProportionalRe asoning_final.pdf 7 th Grade Math Quarter 2 2
1 day 7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent rations in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin Proportions, Cross-Products property. Determine if two quantities are in a proportional relationship from a table. The table below gives the price for different numbers of books. Do the numbers in the table represent a proportional relationship? proportion; cross products; cross products property 4-3 Number of Books Price 1 3 3 9 4 12 7 18 Solution: 2-3 Students can examine the numbers to determine that the price is the number of books multiplied by 3, except for 7 books. The row with seven books for $18 is not proportional to the other amounts in the table; therefore, the table does not represent a proportional relationship. Solving proportions (using cross-products, mental math, and unit rates) 4-4 7.RP.2: Recognize and represent proportional relationships between quantities. An astronaut who weighs 174 pounds on Earth weighs 29 pounds on the moon. If you weigh 102 pounds, how much would you weigh on the moon? 7 th Grade Math Quarter 2 3
3-4 2 2 2 7.RP.2: Recognize and represent proportional relationships between quantities. 7.G.1: Solve problems involving scale drawings of geometric figures., including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.1: Solve problems involving scale drawings of geometric figures., including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: Identifying the unit rate in tables, and graphs, and equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.2c: Represent Proportional relationships with equations 7.RP.2d: Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and 1,r) where r is the unit rate. 7.EE.3: Solve the two-step equations using inverse operations and the distributive property Similar figures, finding missing measures of similar figures A woman is 5 ft. tall and her shadow is 4 ft. long. A nearby tree has a shadow 30 ft. long. How tall is the tree? Maps and Scale Drawings and Activity Lab You are making a scale drawing with a scale of 2 in. = 17 ft. Explain how you find the length of the drawing of an object that has an actual length of 51 ft. Proportional Relationships, using tables, graphs, unit rates Orange prices: 4 lbs. for $8; 6 lbs. for $10, and 10 lbs. for $20. A salesperson used this information to state the oranges are the same price per pound, no matter what size bag they come in. Why is the salesperson wrong? Students solve contextual problems and mathematical problems using rational numbers. Students convert between fractions, decimals, and percents as needed to solve the problem. Students use estimation to justify the polygon; similar polygons; indirect measurement; corresponding sides scale; scale drawing constant of proportionality; proportional relationships percent 4-5 Supplemental materials/activities recommended 4-6 4-7 5-1 7 th Grade Math Quarter 2 4
reasonableness of answers. Your teacher uses different methods of grading quizzes. Your quiz grades are 85%, 9/10, 16/20, 92%, 21/25, and 79%. Write your quiz grades in order from least to greatest. Find the average percent grade of your quizzes. Solving Percent Problems Using Proportions 5-2. 1.5 2.5 Sally has a recipe that needs teaspoon of butter for every 2 cups of milk. If Sally increases the amount of milk to 3 cups of milk, how many teaspoons of butter are needed? Using these numbers to find the unit rate may not be the most efficient method. Students can set up the following proportion to show the relationship between butter and milk. Solution: One possible solution is to recognize that 2 1 = 3 so 1 = x. The amount of butter needed would be 1teaspoons. A second way to solve this proportion is to use cross-multiplication 3 = 2x. Solving for x would give 1teaspoons of butter. Solving Percent Problems Using Equations (finding a whole, finding a part, finding a %) 5-3 7 th Grade Math Quarter 2 5
3 1 day 1 day s 96% of what number is 24? 18% of 90 is what number? What percent of 496 is 124? Applications of percentages (sales tax, tips, commission, etc.) Your lunch bill is $19.75. A 5% sales tax will be added, and you want to give a tip of about 20% of $19.75. Estimate how much you will pay for lunch. Then find about how much tip you should give. Simple Interest (finding, graphing, and comparing) Graph the total simple interest for $500 at 4.5% over 4 years. Finding percent of change (discounts, markups, etc.) A football player gained 1200 yd last season and 900 yd this season. Find the percent of change. State whether the change is an increase or a decrease. 2 All standards taught this semester Review Formative Assessment Lessons: Developing a Sense of Scale http://map.mathshell.org/materials/lessons.php?taskid=456&subpage=problem INTERIM ASSESSMENT 2: DECEMBER 9-13 NOTES/REFLECTION commission; percent error; sales tax principle; simple interest percent of change; mark-up; discount 5-4 5-5 5-6 7 th Grade Math Quarter 2 6