Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR
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1 Mathematics Curricular Guide SEVENTH GRADE SCHOOL YEAR
2 MATHEMATICS SCOPE & SEQUENCE Unit Title Dates Page 1. Ratios and Proportion... IBD Rational Numbers & Prime Factorization... IBD Expressions and Equations... IBD Probability... IBD Surface Area and Volume... IBD Slope... IBD Data... IBD Process Standards & Mathematical Practices ***IBD - IN BUILDING DECISIONS BENCHMARK 1 BENCHMARK 2 BENCHMARK 3 IMPORTANT NOTES 2
3 GRADE 7 MSP TEST MAP AREA OF EMPHASIS MC CP SA TOTAL NUMBER OF 7.1 RATIONAL NUMBERS AND LINEAR EQUATIONS POINTS PROPORTIONALITY AND SIMILARITY SURFACE AREA AND VOLUME PROBABILITY AND DATA ADDITIONAL KEY CONTENT REASONING, PROBLEM SOLVING, AND COMMUNICATION TOTAL NUMBER OF ITEMS TOTAL NUMBER OF POINTS
4 Ratio and Proportions Unit CCSS unit Standard CCSS Lesson & objective Teacher Notes 7.2.B Solve single- and multi-step problems involving proportional relationships and verify the solutions. Day to Day Lessons (Procedure/Scaffolding) Where to See Unit Rate Input Chart to pull all representations together throughout the unit 7.2.C Describe proportional relationships in similar figures and solve problems involving similar figures. 7.2.D Make scale drawings and solve problems related to scale. 7.2.E Represent proportional relationships using graphs, tables, and equations, and make connections among the representations. 7.2.F Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles. 7.2.G Determine the unit rate in a proportional relationship and relate it to the slope of the associated 4 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. 7.RP.A.2 Recognize and represent proportional relationships between quantities. 7.RP.A.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 place and observing whether the graph is a straight line through the origin. 7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.A.2c Represent Representations: Table, Graph, Equations, Written Day 1 share all steps (pg 9 of Progression Document) Introduce another scenario that at each representation will be done together (pg 231) Use as a true GLAD Input Chart each day add a step (ex. put up sentence cards, etc) HOLT 4.1 pg 214 HOLT 4.2 pg 218 ** need to add items that have fractions (ex. ¾ cup flour for every ½ stick butter; if a person walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½ over ¼ per hour, equivalently 2 miles per hour) CMP2 Comparing and Scaling Investigation 2.3 (T- Drive) Formative D-TAILS mini-lesson Input Chart (T-Drive) Is It Proportional? Give tables, situations Graph Yes/No if through origin, linear, proportional (pg 314 #2a,b; pg 315 #4; pg 315 additional Assessment (Formative and Summative) reflect back to essential questions Formative 1 pg 215 Additional Example #2 pg 222 Warm Up #2 pg 346 (6 th grade book) use table pints of paint What is the unit rate? pg 219 Additional Example #2 Formative 2 pg 317 Lesson Quiz #3b, c and add what is unit rate and how do you
5 line. 7.2.HDetermine whether or not a relationship is proportional and explain your reasoning. proportional relationships by equations. 7.RP.A.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.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. example #4; Unit Rate in a Graph Using the work from Is It Proportional identify the unit rate Have students find a rule for identify on a graph [discover (1, r)] Formative Unit Rate in Equation Go back to all graphs, tables and write equations from prior problems Table: CMP 2.3 write an equation Graphs: Is It Proportional, Unit Rate in Graphs write an equation Verify equations by using a number from the table to check if it works Work on substituting HOLT 1.6 pg 32 know Formative 3 pg 367 Real World Connection Corn pg 365 #5 add to worksheet so it says Dennis deposits money made from corn sells Project/MEC Unit Scenarios All items students will make a table, graph, an equation, written, find the unit rate, and identify if scenario is proportional or not (if you can prove that item is not proportional with one representation then you may stop) Scenarios Whole Group Item Super Blocks (T-Drive: Math: 7 th Grade: 13-14: Ratio Unit) Increasing Pattern 1 (scan from Carolynn binder) Travel (8 th grade HOLT pg 142) Conservation (8 th grade HOLT pg 142) Physical Science (8 th grade HOLT pg 142) Color Tiles Pattern 3 (scan from Carolyn binder) Summative Assessment pg (unit rate from scenario) pg 270 #5 (unit rate & extending proportions in table) leave in table 9:3 and 12:4 blank one above, one below 5
6 Toothpick Triangles (scan from Carolynn binder) non-proportional Increasing Pattern 2 (scan from Carolynn binder) non-proportional Problem Solving Worksheets 4.1 or 4.2 One Centimeters to Inches (scan from Rachel It s All Connected) Multi-Step Ratio and Unit Rate Problems Teacher discretion but maybe students have to complete two of the following Scenarios Lawn Mowing Cat Food Missing Paints Photographs Cereal HOLT 6.6 pg 358 HOLT 6.7 pg 362 Formative Percent Real World Connection Corn Add #5 from pg 365 change so it reads Dennis deposits money made from corn sells. pg 221 #2 in Lesson Quiz Performance task Cellphone dilemma(locat ed on S:Drive) VOCABULARY: Ratio Rate Unit Rate Scale Scale Factor Proportion Interest Percent Percent Increase Percent Decrease Simple Interest 6
7 Rational Numbers Unit based on WA STATE standards Standards CCSS Lesson & Objective Teacher Notes 7.1.A Compare and order rational numbers using the number line, lists, and the symbols <, >, or =. 7.1.B Represent +, -, x, of positive and negative integers visually and numerically 7.1.C Fluently and accurately +, -, x, rational numbers 7.1.D Define and determine absolute value of a number 7.1.G Solve single and multi-step word problems involving rational numbers and verify the solution. 7.5.B Write the prime factorization of whole numbers 7.2.A Mentally +, -, x, simple fractions, decimals, and percent 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. d. Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. c. Apply properties of operations as strategies to multiply and divide rational numbers. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Holt: 2-1, 2-2, 2-3,2-4,2-5,2-6, ,3-2,3-3,3-4,3-5, 3-7,3-8,3-9,3-10,3-11 Quiz after 2-5 Integers Summative Assessment After 2-11 Quiz after 3-11 over chapter 3 VOCABULARY: Integer Rational Number Absolute Value Opposite Prime Factorization Prime Number 7
8 Expression and Equations CCSS unit Standards CCSS Lesson & Objective Teacher Notes 7.1.E Solve two-step linear equations. 7.1.F "Write an equation that corresponds to a given problem situation, and describe a problem situation that corresponds to a given equation. Note: Items only include equations in the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers to represent CCSS 7.EE.4." Expressions and Equations 7.EE Use properties of operations to generate equivalent expressions. 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Holt 1-4, 1-5, (operations and properties) 1-6, 1-7, 1-8, 1-9, 1-10, 1-11(variables, expressions, and one step equations) 12-1, 12-2, 12-3, (two step linear equations) Chapter 1 Ready to Go On? Quiz Chapter 12 - Ready to Go On? Quiz Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the 12-4, 12-5, 12-6, 12-7 (inequalities) PERFORMANCE TASK VOCABULARY: Sweet Algebra (Located on S:Drive) Equation Expression Inverse Operation Constant Solution Order of Operation Inequality Solution Set 8
9 center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: 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. 9
10 Probability Unit based on WA STATE standards Standards CCSS Lesson & Objective Teacher Notes 7.4.A Represent the sample space of probability experiments in multiple ways, including tree diagrams and organized lists. 7.4.B Determine theoretical probability of a particular event and use theoretical probability to predict experimental outcomes. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly200 times. 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. CMP2 WDYE Problems 1-2, 1-2, 1-3, 2-1, 2-2, Area Model Practice pg 35 ACE # , 3-1 Holt 11-1, 11-2, 11-3, 11-4, 11-5 Chapter 11 Ready to Go On?Quiz A VOCABULARY: Event Theoretical Probability Experimental Probability Sample Space Outcome Equally Likely Trial 10
11 Surface area and Volume Unit based on WA STATE standards Standards CCSS Lesson & Objective Teacher Notes 7.3.A Determine the surface area and volume of cylinders using the appropriate formulas and explain why the formulas work 7.3.B Determine the volume of pyramids and cones using formulas 7.3.C Describe the effect that a change in scale factor on one attribute of a two- or threedimensional figure has on other attributes of the figures, such as the side or edge length, perimeter, area, surface area, or volume of a geometric figure 7.3.D Solve single or multistep word problems involving surface area or volume and verify the solutions 7.G.6 - Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Holt 10-2, 10-3, 10-4, 10-6 Performance task--- thematics/default.aspx VOCABULARY: Base Cone Cylinder Edge Face Prism Pyramid Surface Area Volume 11
12 Slope Unit based on WA STATE standards Standards CCSS Lesson & Objective Teacher notes 7.2.F Determine the slope of a line corresponding to the graph of a proportional relationship and relate slope to similar triangles. 7.RP.2 Recognize and represent proportional relationships between quantities. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Holt 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7, 5-8 The language of determining slope moves to grade 8 CCSS-M (8.EE.5 & 8.EE.6). This WA PE remains on the MBA through because it is assessed on the Grade 7 MSP. pg 320 #6-8 OR 5.6 Lesson Quiz pg 306 VOCABULARY: Slope Rate of Change Input Output Origin Linear X-axis Y-axis Intercepts Quadrant 12
13 Data Unit based on WA STATE standards Standards CCSS Lesson & Objective Teacher Notes 7.4.C Describe a data set using measures of center (median, mean, and mode) and variability (maximum, minimum, and range) and evaluate the suitability and limitations of using each measure for different situations. 7.4.D Construct and interpret histograms, stem-and-leaf plots, and circle graphs. 7.4.E Evaluate different displays of the same data for effectiveness and bias, and explain reasoning. Holt 7-1, 7-2, 7-3, 7-4, 7-6, 7-7, 7-10, VOCABULARY: Bar Graph Circle Graph Histogram Stem-and-Leaf Plot Mean Median Mode Range Minimum Maximum Outlier 13
14 Process Standards Standards 7.6.A Analyze a problem situation to situation to determine the question(s) to be answered. 7.6.B Identify relevant, missing, and extraneous information related to the solution. 7.6.C Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem. 7.6.D Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution. 7.6.E Communicate the answer(s) to the question(s) in a problem using appropriate representation, including symbols and informal and formal mathematical language. Unit based on WA STATE standards CCSS 1. Make sense of problems ad 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. 7.6.F Apply a previously used problem-solving strategy in a new context. 7.6.G Extract and organize 14
15 mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. 7.6.H Make and test conjectures based on data (or information) collected from explorations and experiments. 15
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