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### NR Numerical Reasoning

- Place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions
- 5.NR.1 Use place value understanding to solve real-life, mathematical problems.
- 5.NR.1.1 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.
- 5.NR.1.2 Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 10
^{3}.

- 5.NR.2 Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.
- 5.NR.2.1 Fluently multiply multi-digit (up to 3-digit by 2-digit) whole numbers to solve authentic problems.
- 5.NR.2.2 Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.

- 5.NR.3 Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
- 5.NR.3.1 Explain the meaning of a fraction as division of the numerator by the denominator (
*a/b*=*a*÷*b*). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. - 5.NR.3.2 Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.
- 5.NR.3.3 Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.
- 5.NR.3.4 Model and solve problems involving multiplication of a fraction and a whole number.
- 5.NR.3.5 Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
- 5.NR.3.6 Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

- 5.NR.3.1 Explain the meaning of a fraction as division of the numerator by the denominator (
- 5.NR.4 Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems.
- 5.NR.4.1 Read and write decimal numbers to the thousandths place using base ten numerals written in standard form and expanded form.
- 5.NR.4.2 Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- 5.NR.4.3 Use place value understanding to round decimal numbers to the hundredths place.
- 5.NR.4.4 Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.

- 5.NR.5 Write, interpret, and evaluate numerical expressions within authentic problems.
- 5.NR.5.1 Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.

- 5.NR.1 Use place value understanding to solve real-life, mathematical problems.

### PAR Patterning & Algebraic Reasoning

- Generating patterns, plotting ordered pairs in the first quadrant
- 5.PAR.6 Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).
- 5.PAR.6.1 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.
- 5.PAR.6.2 Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.

- 5.PAR.6 Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).

### MDR Measurement & Data Reasoning

- Measurements within the metric system, measurement conversions and time as a unit of measurement
- 5.MDR.7 Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.
- 5.MDR.7.1 Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.
- 5.MDR.7.2 Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
- 5.MDR.7.3 Convert among units within the metric system and then apply these conversions to solve multistep, practical problems.
- 5.MDR.7.4 Convert among units within relative sizes of measurement units within the customary measurement system.

- 5.MDR.7 Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.

### GSR Geometric & Spatial Reasoning

- Properties of polygons and rectangular prisms, classify polygons
- 5.GSR.8 Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
- 5.GRS.8.1 Classify, compare, and contrast polygons based on properties.
- 5.GRS.8.2 Determine, through exploration and investigation, that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.
- 5.GRS.8.3 Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.
- 5.GRS.8.4 Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.

- 5.GSR.8 Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.