5th

Number Sense and Base Ten

Number Sense and Operations – Fractions

Algebraic Thinking and Operations

Geometry

Measurement and Data Analysis

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.

Use whole number exponents to explain:

Round decimals to any given place value within thousandths.

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

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

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. 

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

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

Solve real-world problems involving addition and subtraction of fractions with unlike denominators.

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).

Extend the concept of multiplication to multiply a fraction or whole number by a fraction.

Justify the reasonableness of a product when multiplying with fractions. 

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

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

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

Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).

Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases. 

Investigate the relationship between two numerical patterns.

Define a coordinate system.

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

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

Classify two-dimensional figures in a hierarchy based on their attributes.

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.

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

Understand the concept of volume measurement.

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

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

Patterns in the number of zeroes of the product when multiplying a number by powers of 10

Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths

Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product

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

Estimate the size of the product based on the size of the two factors

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

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

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

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

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

Generate two numerical patterns given two rules and organize in tables

Translate the two numerical patterns into two sets of ordered pairs

Graph the two sets of ordered pairs on the same coordinate plane

Identify the relationship between the two numerical patterns.

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

Any point on the coordinate plane can be represented by its coordinates

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

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

Recognize volume as an attribute of right rectangular prisms

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

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