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CO.5.1.Number Sense, Properties, and Operations
Number Sense, Properties, and Operations
5.1.1. The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms. Students can:5.1.1.a. Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. (CCSS: 5.NBT.1)5.1.1.a.i. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. (CCSS: 5.NBT.2)
5.1.1.a.ii. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. (CCSS: 5.NBT.2)
5.1.1.a.iii. Use whole-number exponents to denote powers of 10. (CCSS: 5.NBT.2)
5.1.1.b. Read, write, and compare decimals to thousandths. (CCSS: 5.NBT.3)5.1.1.b.i. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. (CCSS: 5.NBT.3a)Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals
5.1.1.b.ii. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (CCSS: 5.NBT.3b)
5.1.1.c. Use place value understanding to round decimals to any place. (CCSS: 5.NBT.4)Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding
5.1.1.d. Convert like measurement units within a given measurement system. (CCSS: 5.MD)5.1.1.d.i. Convert among different-sized standard measurement units within a given measurement system. (CCSS: 5.MD.1)Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement
5.1.1.d.ii. Use measurement conversions in solving multi-step, real world problems. (CCSS: 5.MD.1)Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement
5.1.2. Formulate, represent, and use algorithms with multi-digit whole numbers and decimals with flexibility, accuracy, and efficiency. Students can:5.1.2.a. Fluently multiply multi-digit whole numbers using standard algorithms. (CCSS: 5.NBT.5)Quiz, Flash Cards, Worksheet, Game & Study Guide Division Quiz, Flash Cards, Worksheet, Game & Study Guide Odd/Even
5.1.2.b. Find whole-number quotients of whole numbers. (CCSS: 5.NBT.6)5.1.2.b.i. Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. (CCSS: 5.NBT.6)Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra Quiz, Flash Cards, Worksheet, Game & Study Guide Division Quiz, Flash Cards, Worksheet, Game & Study Guide Division Quiz, Flash Cards, Worksheet, Game & Study Guide Division
5.1.2.b.ii. Illustrate and explain calculations by using equations, rectangular arrays, and/or area models. (CCSS: 5.NBT.6)Quiz, Flash Cards, Worksheet, Game & Study Guide Division Quiz, Flash Cards, Worksheet, Game & Study Guide Division Quiz, Flash Cards, Worksheet, Game & Study Guide Division
5.1.2.c. Add, subtract, multiply, and divide decimals to hundredths. (CCSS: 5.NBT.7)5.1.2.c.i. Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 5.NBT.7)
5.1.2.c.ii. Relate strategies to a written method and explain the reasoning used. (CCSS: 5.NBT.7)
5.1.2.d. Write and interpret numerical expressions. (CCSS: 5.OA)5.1.2.d.i. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (CCSS: 5.OA.1)
5.1.2.d.ii. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. (CCSS: 5.OA.2)
5.1.3. Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency. Students can:5.1.3.a. Use equivalent fractions as a strategy to add and subtract fractions. (CCSS: 5.NF)5.1.3.a.ii. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with like denominators. (CCSS: 5.NF.1)
5.1.4. The concepts of multiplication and division can be applied to multiply and divide fractions (CCSS: 5.NF). Students can:5.1.4.a. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). (CCSS: 5.NF.3)Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions Quiz, Flash Cards, Worksheet, Game & Study Guide Number Line Quiz, Flash Cards, Worksheet, Game & Study Guide Probability Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
5.1.4.b. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (CCSS: 5.NF.3)
5.1.4.c. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. In general, (a/b) × (c/d) = ac/bd. (CCSS: 5.NF.4a)
5.1.4.d. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. (CCSS: 5.NF.4b)5.1.4.d.i. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. (CCSS: 5.NF.4b)
5.1.4.e. Interpret multiplication as scaling (resizing). (CCSS: 5.NF.5)5.1.4.e.i. Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. (CCSS: 5.NF.5a)
5.1.4.e.ii. Apply the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. (CCSS: 5.NF.5b)Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
5.1.4.f. Solve real world problems involving multiplication of fractions and mixed numbers. (CCSS: 5.NF.6)
5.1.4.g. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. (CCSS: 5.NF.7a)
5.1.4.h. Interpret division of a whole number by a unit fraction, and compute such quotients. (CCSS: 5.NF.7b)5.1.4.h.i. Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions. (CCSS: 5.NF.7c)
CO.5.2.Patterns, Functions, and Algebraic Structures
Patterns, Functions, and Algebraic Structures
5.2.1. Number patterns are based on operations and relationships. Students can:5.2.1.a. Generate two numerical patterns using given rules. (CCSS: 5.OA.3)Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns
CO.5.4.Shape, Dimension, and Geometric Relationships
Shape, Dimension, and Geometric Relationships
5.4.1. Properties of multiplication and addition provide the foundation for volume an attribute of solids. Students can:5.4.1.a. Model and justify the formula for volume of rectangular prisms. (CCSS: 5.MD.5b)5.4.1.a.i. Model the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes. (CCSS: 5.MD.5b)Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
5.4.1.a.iii. Represent threefold whole-number products as volumes to represent the associative property of multiplication. (CCSS: 5.MD.5a)Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
5.4.1.b. Find volume of rectangular prisms using a variety of methods and use these techniques to solve real world and mathematical problems. (CCSS: 5.MD.5a)5.4.1.b.i. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (CCSS: 5.MD.4)Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
5.4.1.b.ii. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths. (CCSS: 5.MD.5b)Quiz, Flash Cards, Worksheet, Game & Study Guide Volume
5.4.2. Geometric figures can be described by their attributes and specific locations in the plane. Students can:5.4.2.a. Graph points on the coordinate plane to solve real-world and mathematical problems. (CCSS: 5.G)Quiz, Flash Cards, Worksheet, Game & Study Guide Coordinates Quiz, Flash Cards, Worksheet, Game & Study Guide Coordinates Quiz, Flash Cards, Worksheet, Game & Study Guide Plot Points
5.4.2.b. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. (CCSS: 5.G.2)Quiz, Flash Cards, Worksheet, Game & Study Guide Coordinates Quiz, Flash Cards, Worksheet, Game & Study Guide Coordinates Quiz, Flash Cards, Worksheet, Game & Study Guide Plot Points
5.4.2.c. Classify two-dimensional figures into categories based on their properties. (CCSS: 5.G)5.4.2.c.i. Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. (CCSS: 5.G.3)Quiz, Flash Cards, Worksheet, Game & Study Guide Area Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter Quiz, Flash Cards, Worksheet, Game & Study Guide Shapes
5.4.2.c.ii. Classify two-dimensional figures in a hierarchy based on properties. (CCSS: 5.G.4)Quiz, Flash Cards, Worksheet, Game & Study Guide Area Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter Quiz, Flash Cards, Worksheet, Game & Study Guide Shapes