Common Core Math 7 Year at Glance

Transcription

1 ! Common Core Math 7 Year at Glance WHAT STUDENTS LEARN IN SEVENTH GRADE Grade 7 CA Framework Draft Overview In grade seven instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships, including percentages; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. Students also work towards fluently solving equations of the form px + q = r and p(x + q) = r. (1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. (2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. (3) Students continue their work with area from grade six, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in grade eight they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 1

2 (4) Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences (The Common Core State Standards Initiative [CCSSI] 2010, Grade 7 Introduction). Essential Learning for the Next Grade In middle school, multiplication and division develop into powerful forms of ratio and proportional reasoning. The properties of operations take on prominence as arithmetic matures into algebra. The theme of quantitative relationships also becomes explicit in grades six through eight, developing into the formal notion of a function by grade eight. Meanwhile, the foundations of high school deductive geometry are laid in the middle grades. The gradual development of data representations in kindergarten through grade five leads to statistics in middle school: the study of shape, center, and spread of data distributions; possible associations between two variables; and the use of sampling in making statistical decisions (Adapted from PARCC 2012). To be prepared for grade eight mathematics students should be able to demonstrate they have acquired certain mathematical concepts and procedural skills by the end of grade seven and have met the fluency expectations for the grade seven. Seventh grade students are expected to fluently solve equations of the form px + q = r and p(x + q) = r (7.EE.4 ), which also requires fluency with rational number arithmetic (7.NS.1 3 ), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1 ). Also adding, subtracting, multiplying and dividing rational numbers (7.NS.1 2 ) is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade eight, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade seven depends on rational number arithmetic, fluency with rational number arithmetic should also be the goal in grade seven. These fluencies and the conceptual understandings that support them are foundational for work in grade eight. Of particular importance for students to attain in grade seven are skills and understandings to analyze proportional relationships and use them to solve real-world and mathematical problems (7.RP.1-3 ); apply and extend previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers (7.NS.1-3 ); use properties of operations to generate equivalent expressions (7.EE.1-2 ); and solve real-life and mathematical problems using numerical and algebraic expressions and equations (7.EE.3-4 ). IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 2

3 ! Grade 7 Mathematics Year at Glance Unit Length 1 Week Aug. 11 th 8 Weeks Aug. 18 th to Oct. 3 rd units 1 & 2 5 Weeks Oct. 6 th to Nov. 7 th Unit Name & Sub-topics Introductory Week Setting the tone Establishing Routines Problem Solving/ Math Practice focus Unit 1: Proportional Relationships Unit Rates with complex fractions Understanding the constant of proportionality in tables, graphs, equations, diagrams and verbal descriptions Understanding what proportional means Application Problems involving proportions Scale Figures Unit 2: Rational Numbers Integer Operations Integers on a number line Standards Addressed M = Major Cluster A/S = Additional or Supporting Cluster (M) 7.RP.1, 2 (A/S) 7.G.1 (M) 7.NS.2d (M) 7.NS.1, 2, 3 (less 2d) Prior Knowledge Expected Fluencies From Grade 6 Not Listed Within Units: Multi-Digit Whole Number Division (6.NS.2) 1-week pre-unit on crossproducts and equivalent fractions. Multiply and Divide Fractions (6.NS.1) Solving 1-Step Equations Work with Ratios between Tables, Graphs, Equations; Multiplicative Relationship (6.RP.3a; 6.RP.3b) Ability to Use Ratio Concepts to Solve Problems (6.RP.1 3) Unit Conversions within Systems (6.RP.3d) Add and Subtract Fractions Decimal Operations Understanding the System Assessment Guideline Unit 1 assessment Q #15 & 16 cover 7RP3 Unit 2 assessment IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 3

4 unit 2 Add, Subtract, Multiply, and Divide Rational Numbers in Context of Rational Numbers (6.NS.5 8) Opposites and Absolute Value (6.NS.6a; 6.NS.7c) 4 Weeks Nov. 12 th to Dec. 12 th units 3 & 4 Dec Weeks Jan. 5 th to Jan. 23 rd units 1: component 6 & 4: Unit 3: Expressions, Equations and Inequalities Write, Add, Subtract and Factor Linear Expressions Solve Multi-step Equations and Inequalities Identify Sequence of Operations Used in Solving Solve Word Problems involving Equations and Inequalities Graph and Interpret the Solution Set of an Inequality Review, catch up or move forward Unit 4: Percentages Solve multi-step problems involving percents; tax, commission, tip, percent increase/decrease, interest, Decimal to fraction to percent conversions (M) 7.EE.1, 2, 3, 4 (M) 7.RP.3 (M) 7.EE.4 2-week pre-unit, writing expressions, n-box, algebra tiles and solving with algebra tiles. Properties Distributive Property with Area Models and Factoring (6.EE.3) Extension of Arithmetic to Algebraic Expressions (6.EE.1 4) Reason and Solve One- Variable Equations and Inequalities (6.EE.5 8) Represent and Analyze Quantitative Relationships (6.EE.9) Unit 3 Assessment Unit 4 Assessment May consider Q #15 & 16 from unit 1 assessment IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 4

5 component Weeks Jan. 26 th to Feb. 20 th unit 5 3 Weeks Feb. 23 rd to Mar. 13 th units 6 & 7 Mar Unit 5: Probability Understand that Probability is between 0 and 1 Approximate Probability and Predict Relative Frequency Develop Probability Models Compare Theoretical and Experimental Probability Sample Space Unit 6: Sampling and Comparing Distributions Sampling Central Tendency Mean Absolute Deviation Review, catch up or move forward (A/S) 7.SP.5, 6, 7, 8 7.SP.1, 2 (A/S) 7.SP 3, 4 (A/S) Fraction Operations (6.NS.1, 5.NS.4) Decimal Operations (6.NS.3) Mean Absolute Deviation (6.SP.5c) Unit 5 assessment Unit 6 Assessment Unit 7 Assessment May give them separately or following the standard 2 Weeks Apr. 6 th to Apr. 17 units 8: Component 3 & 9: component 1 Unit 7: Angles & Building Shapes Draw Geometric Shapes with Given Conditions Writing and Solving Equations Involving Missing Angle Measures in Figures (A/S) 7.G.2, 5 Performance Task or OARs assessments IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 5

6 3 Weeks Apr. 20 th to May 8th units 8 & 9 Unit 8: 2-D & 3-D Geometry Real World Problems Involving Area and Perimeter Surface Area of Cubes and Right Rectangular Prisms Volume of Cubes and Right Rectangular Prisms Formulas for Circumference and Area of Circles 2-D cross sections of 3-D shapes (A/S) 7.G.1, 3, 4, 6 v 1-2 week pre-unit from prior grades volume and surface area Volume of Rectangular Prisms (6.G.2) Surface Area (6.G.4) Unit 8 assessment Unit 9 assessment May be given separately following the standards or together at the end v Indicates pre- units to be taught to address standards that were taught in prior grades, but have moved grade levels for which students need a first- teaching, or in which students need review. Pre- units phased out over time. IMP CC Math 7 Course Outline FUESD Seventh Grade Math Instructional Timeline 6