Number Sense and Base Ten

• 5.NSBT.1 Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1/10 times what the same digit represents in the place to its left.

• 5.NSBT.2 Use whole number exponents to explain:

  • a. patterns in the number of zeroes of the product when multiplying a number by powers of 10;

  • b. patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

• 5.NSBT.3 Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <.

• 5.NSBT.4 Round decimals to any given place value within thousandths.

• 5.NSBT.5 Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm.

• 5.NSBT.6 Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division.

• 5.NSBT.7 Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings.

 

Number Sense and Operations - Fractions

• 5.NSF.1 Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line.

• 5.NSF.2 Solve real-world problems involving addition and subtraction of fractions with unlike denominators.

• 5.NSF.3 Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., 𝑎/𝑏 = 𝑎 ÷ 𝑏).

• 5.NSF.4 Extend the concept of multiplication to multiply a fraction or whole number by a fraction.

  • a. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths;

  • b. Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product;

  • c. Interpret multiplication in which both factors are fractions less than one and compute the product.  

• 5.NSF.5 Justify the reasonableness of a product when multiplying with fractions.

  • a. Estimate the size of the product based on the size of the two factors;

  • b. Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number;

  • c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number;

  • d. Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1.

• 5.NSF.6 Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number.

• 5.NSF.7 Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations.

  • a. Interpret division of a unit fraction by a non-zero whole number and compute the quotient;

  • b. Interpret division of a whole number by a unit fraction and compute the quotient.

• 5.NSF.8 Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations. 

 

Algebraic Thinking and Operations

• 5.ATO.1 Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).

• 5.ATO.2 Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases.

• 5.ATO.3 Investigate the relationship between two numerical patterns.

  • a. Generate two numerical patterns given two rules and organize in tables;

  • b. Translate the two numerical patterns into two sets of ordered pairs;

  • c. Graph the two sets of ordered pairs on the same coordinate plane;

  • d. Identify the relationship between the two numerical patterns.

 

Geometry

• 5.G.1 Define a coordinate system.

  • a. The x- and y- axes are perpendicular number lines that intersect at 0 (the origin);

  • b. Any point on the coordinate plane can be represented by its coordinates;

  • c. The first number in an ordered pair is the x-coordinate and represents the horizontal distance from the origin;

  • d. The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin.

• 5.G.2 Plot and interpret points in the first quadrant of the coordinate plane to represent realworld and mathematical situations.

• 5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

• 5.G.4 Classify two-dimensional figures in a hierarchy based on their attributes.

 

Measurement and Data Analysis

• 5.MDA.1 Convert measurements within a single system of measurement: customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., mm, cm, m, km, g, kg, mL, L) from a larger to a smaller unit and a smaller to a larger unit.

• 5.MDA.2 Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot.

• 5.MDA.3 Understand the concept of volume measurement.

  • a. Recognize volume as an attribute of right rectangular prisms;

  • b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes;

  • c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes.

• 5.MDA.4 Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation.