# HPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means:

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1 Number and Numeration MA.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. ) MA.7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. ) MA.7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers.) Quarter 1 N.FL Solve problems involving operations with integers. N.FL Add, subtract, multiply, and divide positive and negative rational numbers fluently. N.FL Estimate results of computations with rational numbers. Students will be able to solve problems with positive or negative numbers. Lessons this Quarter 40 1 Students will be able to add, subtract, multiply, and divide positive and negative fractions, and percentages. 1 Students will be able to estimate the answer of math problems with fractions, decimals, and percentages., Games, Brochures, Games, Brochures evaluate simplify integers expression/equation additive inverse rational number additive and multiplicative identities additive and multiplicative inverses commutative property associative property distributive property Page 1 of 10

2 Algebra MA.7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) MA.7.EE.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.) A.PA Understand and use basic properties of real numbers: additive and multiplicative identities, additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition. Students will be able to solve problems when given specific addition and multiplication rules of math. Page 2 of 10

3 MA.7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.) Quarter 2 Number and Numeration MA.7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. N.FL Calculate rates of change including speed. Students will be able to compare how amounts change over time. Ex: miles per hour Lessons this Quarter 30 unit rate scaling proportion Page 3 of 10

4 MA.7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. N.FL Convert ratio quantities between different systems of units, such as feet per second to miles per hour. Students will be able to change from one unit of measure to another. 10 equivalent rate ratio square root MA.7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. MA.7.RP.2. Recognize and represent proportional relationships between quantities. N.FL.07.0 Solve proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables. Students will be able to find equal amounts using 2 fractions. 10 cube root perfect square radical sign dimensions parallelograms protractor compass similar Moving to a different Grade N.MR Understand the concept of square root and cube root, and estimate using calculators. Students will be able to use a calculator to find out which number multiplied by itself 2 or 3 times equals a given number. corresponding sides congruent scale factor Geometry Page 4 of 10

5 MA.7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. MA.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. G.SR Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specified dimensions. G.TR Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. Students will be able to draw a shape using a ruler and other tools. Students will understand that similar shapes, whether bigger or smaller, have the same angles, and their sides have an equal relationship., Graphing Activity Page of 10

6 MA.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. G.TR Solve problems about similar figures and scale drawings. Students will be able to solve problems with similar shapes. 10, Mapping MA.7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. G.TR.07.0 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments. Students will be able to show that two triangles are alike, when given rules of triangles. MA.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. G.TR Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r2. Students will understand that there is a relationship between the area and sides of 2 matching triangles. Page 6 of 10

7 Quarter 3 Data and Probability MA.7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. D.AN Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-and-whisker plots, and select appropriate representation to address specific questions. Students will be able to create and answer questions about different types of graphs. Lessons this Quarter 2 1, Surveys, Posters mean median mode range IQR stem and leaf plot histograms box and whisker graphs relative frequency cumulative frequency quartile outlier extremes Page 7 of 10

8 MA.7.G.3. Describe the twodimensional figures that result from relative frequencies and cumulative D.AN Calculate and interpret slicing three-dimensional figures, as in frequencies for given data sets. plane sections of right rectangular prisms and right rectangular pyramids. MA.7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Students will be able to figure out how often something is supposed to happen and then compare it to how often it actually does happen after doing an experiment. D.AN Find and interpret the Students will be able to split median, quartiles, and interquartile range information into quarters. of a given set of data. MA.7.G.. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. Page 8 of 10

9 Algebra MA.7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of twoand three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. A.FO From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. Students will be able to create a rule and/or graph it when given a starting amount and a constant increase or decrease, and then use that to solve problems. 1 Quarter 4 Lessons this Quarter Algebra 3 MA.7.RP.2. Recognize and represent proportional relationships between quantities. A.RP Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. Students will be able to create equations using data from a story problem or graph involving constant pattern. slope rise run x and y intercepts like terms Page 9 of 10

10 MA.7.RP.2. Recognize and represent proportional relationships between quantities. A.PA For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of wather in a tank being filled at a constant rate; degrees celsius and degrees fahrenheit; distance and time under constant speed. Students will be able to solve problems using graphs and equations involving constant pattern. unlike terms A.PA Represent linear functions in the form y=x + b, y=mx, and y=mx+b, and graph, interpreting slope and y- intercept. Finding and graphing slope/ steepness 20, Graph Boards MA.7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) A.FO Add, subtract and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) x + y, or 2x (x 4), and justify using properties of real numbers. Common core standards not aligned with GLCE Moved to a different grade Moved to a different quarter Students will be able to combine like terms in problems. Page 10 of 10

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