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### 5.NBT Number Sense and Operations in Base Ten

- 5.NBT.A Use place value system understanding to perform operations with multi-digit whole numbers to billions and decimals to thousandths.
- 5.NBT.A.1 Read, write and identify numbers from billions to thousandths using number names, base ten numerals and expanded form.
- 5.NBT.A.2 Compare two numbers from billions to thousandths using the symbols >, = or <, and justify the solution.
- 5.NBT.A.3 Understand that in a multi-digit number, a digit represents 1/10 times what it would represents in the place to its left.
- 5.NBT.A.4 Evaluate the value of powers of 10 and understand the relationship to the place value system.
- 5.NBT.A.5 Round numbers from billions to thousandths place.
- 5.NBT.A.6 Add and subtract multi-digit whole numbers and decimals to the thousandths place, and justify the solution.
- 5.NBT.A.7 Multiply multi-digit whole numbers and decimals to the hundredths place, and justify the solution.
- 5.NBT.A.8 Divide multi-digit whole numbers and decimals to the hundredths place using up to two-digit divisors and four-digit dividends, and justify the solution.

### 5.NF Number Sense and Operations in Fractions

- 5.NF.A Understand the relationship between fractions and decimals (denominators that are factors of 100).
- 5.NF.A.1 Understand that parts of a whole can be expressed as fractions and/or decimals.
- 5.NF.A.2 Convert decimals to fractions and fractions to decimals.
- 5.NF.A.3 Compare and order fractions and/or decimals to the thousandths place using the symbols >, = or <, and justify the solution.

- 5.NF.B Perform operations and solve problems with fractions and decimals.
- 5.NF.B.4 Estimate results of sums, differences and products with fractions and decimals to the thousandths.
- 5.NF.B.5 Justify the reasonableness of a product when multiplying with fractions.
- 5.NF.B.5.a Estimate the size of the product based on the size of the two factors.
- 5.NF.B.5.b Explain why multiplying a given number by a fraction greater than 1 results in a product larger than the given number.
- 5.NF.B.5.c Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
- 5.NF.B.5.d Explain why multiplying the numerator and denominator by the same number is equivalent to multiplying the fraction by 1.

- 5.NF.B.6 Solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators, and justify the solution.
- 5.NF.B.7 Extend the concept of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.B.7.a Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths.
- 5.NF.B.7.b Calculate and interpret the product of a fraction by a whole number and a whole number by a fraction.
- 5.NF.B.7.c Calculate and interpret the product of two fractions less than one.

- 5.NF.B.8 Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.
- 5.NF.B.8.a Calculate and interpret the quotient of a unit fraction by a non-zero whole number.
- 5.NF.B.8.b Calculate and interpret the quotient of a whole number by a unit fraction.

### 5.RA Relationships and Algebraic Thinking

- 5.RA.A Represent and analyze patterns and relationships.
- 5.RA.A.1 Investigate the relationship between two numeric patterns.
- 5.RA.A.1.a Generate two numeric patterns given two rules.
- 5.RA.A.1.b Translate two numeric patterns into two sets of ordered pairs.
- 5.RA.A.1.c Graph numeric patterns on the Cartesian coordinate plane.
- 5.RA.A.1.d Identify the relationship between two numeric patterns.

- 5.RA.A.2 Write a rule to describe or explain a given numeric pattern.

- 5.RA.A.1 Investigate the relationship between two numeric patterns.
- 5.RA.B Write and interpret numerical expressions.
- 5.RA.B.3 Write, evaluate and interpret numeric expressions using the order of operations.
- 5.RA.B.4 Translate written expressions into algebraic expressions.

- 5.RA.C Use the four operations to represent and solve problems.
- 5.RA.C.5 Solve and justify multi-step problems involving variables, whole numbers, fractions and decimals.

### 5.GM Geometry and Measurement

- 5.GM.A Classify two- and three-dimensional geometric shapes.
- 5.GM.A.1 Understand that attributes belonging to a category of figures also belong to all subcategories.
- 5.GM.A.2 Classify figures in a hierarchy based on properties.
- 5.GM.A.3 Analyze and describe the properties of prisms and pyramids.

- 5.GM.B Understand and compute volume.
- 5.GM.B.4 Understand the concept of volume and recognize that volume is measured in cubic units.
- 5.GM.B.4.a Describe a cube with edge length 1 unit as a “unit cube” and is said to have “one cubic unit” of volume and can be used to measure volume.
- 5.GM.B.4.b Understand that the volume of a right rectangular prism can be found by stacking multiple layers of the base.

- 5.GM.B.5 Apply the formulas V = l × w × h and V = B × h for volume of right rectangular prisms with whole-number edge lengths.

- 5.GM.B.4 Understand the concept of volume and recognize that volume is measured in cubic units.
- 5.GM.C Graph points on the Cartesian coordinate plane within the first quadrant to solve problems.
- 5.GM.C.6 Define a first quadrant Cartesian coordinate system.
- 5.GM.C.6.a Represent the axes as scaled perpendicular number lines that both intersect at 0, the origin.
- 5.GM.C.6.b Identify any point on the Cartesian coordinate plane by its ordered pair coordinates.
- 5.GM.C.6.c Define the first number in an ordered pair as the horizontal distance from the origin.
- 5.GM.C.6.d Define the second number in an ordered pair as the vertical distance from the origin.

- 5.GM.C.7 Plot and interpret points in the first quadrant of the Cartesian coordinate plane.

- 5.GM.C.6 Define a first quadrant Cartesian coordinate system.
- 5.GM.D Solve problems involving measurement and conversions within a measurement system.
- 5.GM.D.8 Convert measurements of capacity, length and weight within a given measurement system.
- 5.GM.D.9 Solve multi-step problems that require measurement conversions.

### 5.DS Data and Statistics

- 5.DS.A Represent and analyze data.
- 5.DS.A.1 Create a line graph to represent a data set, and analyze the data to answer questions and solve problems.
- 5.DS.A.2 Create a line plot to represent a given or generated data set, and analyze the data to answer questions and solve problems, recognizing the outliers and generating the median.