5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Number and Operations in Base Ten
Understand the place value system.

5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

5.NBT.3 Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form

5.NBT.4Use place value understandings to round decimals to any place.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Number and Operations-Fractions
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3 Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, ex amply by using visual fraction models or equations to represent the problem.

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction:

a. Interpret the product (a/b) x q as a parts of a partition of q into b equals parts; equivalently, as the result of a sequence of operations a x q ÷ b.

b. 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. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.NF.5Interpret multiplication as scaling (resizing), by:

a. Comparing 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.

b. Explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b=(nxa)/(nxb) to the effect of multiplying a/b by 1.

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

Measurement and Data
Convert like measurement units within a given measurement system.

5.MD.1Convert among different-sized standard measurement units within a given measurement system and use these conversion in solving multi-step, real-world problems.

Geometric Measurement: Understand concepts of volume and relate volume to multiplication and to addition.

5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume.

5.MD.5Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.

a. Find the volume of a right rectangular with whole-side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V=l x w x h and V=b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems.

Geometry
Graph points on the coordinate plane to solve real-world and mathematical problems.

5.G.2 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.

Operations and Algebraic Thinking5.OA.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.Number and Operations in Base TenUnderstand the place value system.

5.NBT.2Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.5.NBT.3Read, write, and compare decimals to thousandths.- a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form

Perform operations with multi-digit whole numbers and with decimals to hundredths.5.NBT.4Use place value understandings to round decimals to any place.5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm.5.NBT.7Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Number and Operations-FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.3Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, ex amply by using visual fraction models or equations to represent the problem.5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction:5.NF.5Interpret multiplication as scaling (resizing), by:5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Measurement and DataConvert like measurement units within a given measurement system.

Geometric Measurement: Understand concepts of volume and relate volume to multiplication and to addition.5.MD.1Convert among different-sized standard measurement units within a given measurement system and use these conversion in solving multi-step, real-world problems.5.MD.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.5.MD.5Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.GeometryGraph points on the coordinate plane to solve real-world and mathematical problems.

5.G.2Represent 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.