Grade 5 Math Practice

Generate two numerical patterns using given rules, and identify the relationship between the corresponding terms in the two patterns.

Evaluate expressions using the order of operations, including parentheses, to solve problems.

Write simple expressions that record calculations with numbers and interpret numerical expressions without calculating, e.g., 3 × (17 + 8) without calculating, to represent a problem.

Add and subtract decimals to the hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Divide decimals up to two decimal places, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between multiplication and division.

Divide whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value and the properties of operations.

Interpret division of a unit fraction by a non-zero whole number and compute such quotients. Solve real-world problems by dividing a unit fraction by a whole number.

Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real-world problems by dividing a whole number by a unit fraction.

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b), solving word problems involving division of whole numbers leading to fractional answers.

Solve word problems involving multiplication of a fraction by a whole number and by a fraction, using visual fraction models and equations to represent the problem.

Multiply decimals up to two decimal places, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between multiplication and division.

Multiply multi-digit whole numbers using the standard algorithm, understanding the properties of multiplication.

Understand the relationship between place value and decimal fractions, extending the concept of whole number place value to tenths, hundredths, and thousandths.

Read, write, and compare decimals up to the thousandths place, using both standard and expanded forms.

Round decimals to any place value, including tenths, hundredths, and thousandths, using the rounding rules.

Apply the formulas V = l × w × h and V = B × h for the volume of a right rectangular prism to solve real-world and mathematical problems.

Convert among different-sized standard measurement units within a given measurement system (e.g., convert ft to in, qt to gal).

Convert among different-sized standard measurement units within a given measurement system (e.g., convert cm to m, mL to L).

Interpret numerical expressions without calculating them, understanding the role of parentheses and the order of operations in defining the value of the expression.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

Solve word problems involving the four arithmetic operations, including problems involving fractions or decimals, and problems with constraints on the order of operations.

Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10, and explain patterns in the placement of the decimal point when a whole number is multiplied or divided by a power of 10.

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that this is the same as would be found by multiplying the edge lengths, equivalently using the formula V = l × w × h.

Classify quadrilaterals based on their properties, understanding the hierarchy of quadrilaterals (e.g., squares are rhombuses, rectangles, and quadrilaterals).

Use a coordinate system to represent mathematical and real-world problems, drawing polygons in the first quadrant given the coordinates of the vertices.

Understand a coordinate system where the x-axis and y-axis and the origin are defined. Plot points in the first quadrant based on given ordered pairs.

Understand that volume can be measured by counting unit cubes. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and cubic in.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction, and show that this is the same as would be found by multiplying the edge lengths.

Make a line plot to display a data set of measurements in fractions of a unit (e.g. halves, fourths, eighths). Use the line plot to solve problems involving fractions.