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Appendix I Part 2 Mathematics 5 INSTRUCTION Common Core Student Instruction, Practice and Problem Solving, and Teacher Resource Books: Lesson Sample Classify Two-Dimensional Figures Mathematics 5 INSTRUCTION Common Core Table of Contents Mathematical Practices Handbook .........SMPi Number and Operations Unit 1 Standards in Base Ten ....................1 Lesson 1 Understand Place Value .................. 2 5.NBT.A.1 2 Understand Powers of Ten ................. 8 5.NBT.A.2, 5.NBT.A.1 3 Read and Write Decimals ................. 14 5.NBT.A.3a 4 Compare and Round Decimals ............. 24 5.NBT.A.3b, 5.NBT.A.4 5 Multiply Whole Numbers . ................ 34 5.NBT.B.5 6 Divide Whole Numbers . ................. 42 5.NBT.B.6 7 Add and Subtract Decimals ............... 50 5.NBT.B.7 8 Multiply Decimals ..................... 60 5.NBT.B.7 9 Divide Decimals ....................... 70 5.NBT.B.7 MatH IN 5.NBT.A.1, 5.NBT.A.2, 5.NBT.A.3, 5.NBT.A.4, ACTIon Use Whole Numbers and Decimals ....... 82 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7 Interim Assessment ..................... 90 Unit 2 Number and Operations— Fractions ..................... 93 Lesson 10 Add and Subtract Fractions ............... 94 5.NF.A.1, 5.NF.A.2 11 Add and Subtract Fractions in Word Problems .. 104 5.NF.A.2, 5.NF.A.1 12 Fractions as Division ................... 112 5.NF.B.3 Standards in boldface are the focus standards that address major lesson content. ©Curriculum Associates, LLC Copying is not permitted. Table of Contents iii Table of Contents continued Number and Operations— Unit 2 Standards Fractions continued Lesson 13 Understand Products of Fractions .......... 120 5.NF.B.4a, 5.NF.B.4b 14 Multiply Fractions Using an Area Model ...... 126 5.NF.B.4b, 5.NF.B.4a 15 Understand Multiplication as Scaling ........ 136 5.NF.B.5a, 5.NF.B.5b 16 Multiply Fractions in Word Problems ........ 142 5.NF.B.6 17 Understand Division with Unit Fractions. ...... 152 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c 18 Divide Unit Fractions in Word Problems ...... 158 5.NF.B.7c, 5.NF.B.7a, 5.NF.B.7b MatH IN ACTIon Use Fractions .................... 168 5.NF.A.1, 5.NF.A.2, 5.NF.B.4, 5.NF.B.6, 5.NF.B.7 Interim Assessment .................... 176 Unit 3 Operations and Algebraic Thinking ............ 179 Lesson 19 Evaluate and Write Expressions ............ 180 5.OA.A.1, 5.OA.A.2 20 Analyze Patterns and Relationships ......... 190 5.OA.B.3 MatH IN ACTIon Expressions, Patterns, and Relationships ... 200 5.OA.A.1, 5.OA.A.2, 5.OA.B.3, 5.NBT.B.7, 5.NF.B.6 Interim Assessment .................... 208 Standards in boldface are the focus standards that address major lesson content. iv Table of Contents ©Curriculum Associates, LLC Copying is not permitted. Unit 4 Measurement and Data ......... 211 Standards Lesson 21 Convert Measurement Units . ............. 212 5.MD.A.1, 5.NF.B.7 22 Solve Word Problems Involving Conversions ... 222 5.MD.A.1, 5.NF.B.7 23 Make Line Plots and Interpret Data ......... 232 5.MD.B.2 24 Understand Volume ................... 242 5.MD.C.3a, 5.MD.C.3b, 5.NBT.A.2 25 Find Volume Using Unit Cubes ............ 248 5.MD.C.4, 5.MD.C.5a 26 Find Volume Using Formulas ............. 256 5.MD.C.5a, 5.MD.C.5b, 5.MD.C.5c 27 Find Volume of Composite Figures .......... 264 5.MD.C.5c, 5.MD.C.5a, 5.MD.C.5b MatH IN 5.MD.A.1, 5.MD.C.3a, 5.MD.C.3b, 5.MD.C.4, ACTIon Work with Measurement and Data ....... 272 5.MD.C.5a, 5.MD.C.5b, 5.MD.C.5c, 5.NBT.B.5 Interim Assessment .................... 280 Unit 5 Geometry ................... 283 Lesson 28 Understand the Coordinate Plane .......... 284 5.G.A.1 29 Graph Points in the Coordinate Plane ........ 290 5.G.A.2 30 Classify Two-Dimensional Figures .......... 300 5.G.B.4 31 Understand Properties of Two-Dimensional Figures ............... 308 5.G.B.3 MatH IN ACTIon Work with Geometry and Coordinates .... 314 5.G.A.1, 5.G.A.2, 5.G.B.3, 5.G.B.4 Interim Assessment .................... 322 Glossary ............................ 325 Standards, Grade 5 .................... 337 Standards in boldface are the focus standards that address major lesson content. ©Curriculum Associates, LLC Copying is not permitted. Table of Contents v Lesson 30 Introduction 5.G.B.4 Classify Two-Dimensional Figures Use What You Know In this lesson, you will classify polygons based on their properties. Take a look at this problem. Arrange the polygons below so that a polygon can also be called by the name of the polygon before it. Order them from left to right. A B C a. Complete the table below. Put a check in each box if the polygon has the property listed. Property Polygon A Polygon B Polygon C 4 sides 2 pairs of parallel sides 2 pairs of sides of equal length 4 right angles 4 sides of equal length b. Write the most specific name for each polygon from the list below. quadrilateral parallelogram rectangle square A: B: C: c. How would you arrange the polygons so each shape has all the properties of the shape(s) before it? 300 Lesson 30 Classify Two-Dimensional Figures ©Curriculum Associates, LLC Copying is not permitted. Find Out More Shapes can be classified according to their properties. When you order categories of polygons by their properties, you put them in a hierarchy. A hierarchy organizes categories from the most to least general. One model you can use to show a hierarchy is a Venn diagram. A Venn diagram can show categories and subcategories. This Venn diagram shows that squares have all the properties that rectangles have, plus more. This means all squares are also rectangles. A square is also a parallelogram and a quadrilateral. Quadrilaterals Most general category Parallelograms Rectangles Squares Most specific subcategory You can also use a flow chart to show the hierarchy of quadrilaterals. The most general category is at the left, while the most specific is at the right. This means that a figure that belongs in one category also belongs in all categories to the left. Quadrilaterals Parallelograms Rectangles Squares Reflect 1 How are the flow chart and the Venn diagram alike? How are they different? ©Curriculum Associates, LLC Copying is not permitted. Lesson 30 Classify Two-Dimensional Figures 301 Lesson 30 Modeled and Guided Instruction Learn About Ordering Shapes in a Hierarchy Read the problem below. Then explore different ways to classify figures in a hierarchy. Classify the following triangles from the most general to the most specific: scalene triangle, isosceles triangle, and equilateral triangle. Use a tree diagram to classify them as types of triangles. Model It You can understand the problem by listing the properties of the triangles in a table before arranging them in a tree diagram. Types of Triangles Properties of Sides Isosceles 2 or 3 sides of equal length Scalene no sides of equal length Equilateral 3 sides of equal length Model It You can represent the problem with a tree diagram. A tree diagram can also be used to show a hierarchy. Put the most general category as the top branch. Then put the more specific subcategories as the branches. Triangles Categories Subcategories Subcategory 302 Lesson 30 Classify Two-Dimensional Figures ©Curriculum Associates, LLC Copying is not permitted. Connect It Now you will solve the problem from the previous page by using the table to complete a tree diagram. 2 Why is “Triangles” in the top row of the tree diagram? 3 Write “Scalene” and “Isosceles” in the Triangles second row of the tree diagram at the right. Why are those categories separate? 4 Write “Equilateral” beneath “Isosceles.” Why can all equilateral triangles be classified as isosceles triangles? 5 How can you use a tree diagram to order figures? Try It Use what you learned about ordering figures in a hierarchy to solve this problem. 6 Complete the Venn diagram below to show the hierarchy of isosceles, scalene, and equilateral triangles. Triangles ©Curriculum Associates, LLC Copying is not permitted. Lesson 30 Classify Two-Dimensional Figures 303 Lesson 30 Guided Practice Practice Classifying Two-Dimensional Figures Study the example below. Then solve problems 7–9. Example Create a Venn diagram to show the hierarchy of quadrilaterals, A shape can never be both a hexagon and a polygons, trapezoids, and hexagons. quadrilateral. So these Look at how you could show your work using a Venn diagram. regions do not overlap. Polygons Quadrilaterals Hexagons Trapezoids Pair/Share Recreate the hierarchy with a tree diagram. 7 Look at the tree diagram below. Write a statement about the relationship between acute triangles and equilateral triangles. Triangles Which type of triangle is the most specific? Acute Right Obtuse Pair/Share Equilateral Write a statement about the relationship between acute Solution triangles and obtuse triangles. 304 Lesson 30 Classify Two-Dimensional Figures ©Curriculum Associates, LLC Copying is not permitted. 8 Create a Venn diagram to show the hierarchy of the polygons described in the chart. Polygon Description “At least 2” means Trapezoid quadrilateral with at least 1 pair of parallel sides 2 or more. Isosceles Trapezoid trapezoid with at least 2 sides of equal length Parallelogram quadrilateral with 2 pairs of parallel sides Pair/Share Draw one example of a polygon in each separate category of your Venn diagram. 9 Look at the flow chart below. Quadrilaterals Plane Figures Polygons Pentagons The flow chart is like a tree diagram. But the Hexagons arrows show that the hierarchy moves from Which statement is true? Circle the letter of the correct answer.
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