Grade 5:
Fractions Are Numbers
Grade 5: Fractions Are Numbers
In level 5, students extend previous understandings of whole numbers, fractions, and decimals to explain relationships and computation strategies. They apply this work to solve problems in geometric and measurement contexts.
Module 1:
Place Value Concepts for Multiplication and Division with Whole Numbers
In module 1, students describe place value relationships, express powers of 10 with exponents, convert metric measurements, and multiply and divide by multi-digit numbers. They develop fluency with the standard algorithm for multiplication.
TOPIC A
Place Value Understanding for Whole Numbers
Students use multiplicative comparison statements to explain that a digit in one place represents 10 times as much as what it represents in the place to the right. Students notice how digits of a number shift when they multiply or divide by a power of 10 and express a power of 10 in exponential form. Then students find products and quotients by using powers of 10 and convert metric measurements from larger to smaller units.
TOPIC B
Multiplication of Whole Numbers
Students build fluency with multiplying multi-digit numbers by using the standard algorithm. They use place value understanding to visualize the decomposition of factors while they multiply a single digit at a time by another single digit in the standard algorithm.
TOPIC C
Division of Whole Numbers
Students use methods based on place value to find quotients of whole numbers with up to four-digit dividends and two-digit divisors. They estimate quotients, then use tape diagrams, area models, and vertical form to record quotients and remainders.
TOPIC D
Multi-Step Problems with Whole Numbers
Students move between written, pictorial, and numeric representations of mathematical statements. They use tape diagrams to determine when parentheses are needed in expressions and evaluate expressions containing grouping symbols.
Module 2: Addition and Subtraction with Fractions
Module 2 enhances students’ prior work with fractions to add and subtract fractions and mixed numbers with unlike denominators. Students also interpret a fraction as the result of dividing the numerator by the denominator and interpret data in line plots.
TOPIC A
Fractions and Division
Students use equal sharing to understand a fraction as the result of dividing the numerator by the denominator. They use models and vertical form to divide and express quotients as mixed numbers or as fractions. Then students solve word problems involving division.
TOPIC B
Addition and Subtraction of Fractions by Making Like Units
Students use models and equations to make like units before they add and subtract fractions. They analyze expressions to determine whether the units in fractions are related or unrelated, which indicates whether one or more fractions must be renamed to make like units.
TOPIC C
Addition and Subtraction of Fractions, Whole Numbers, and Mixed Numbers
Students apply knowledge of addition and subtraction of whole numbers to help them add and subtract mixed numbers. They use familiar models such as a number bond, a number line, and the arrow way to show their thinking.
TOPIC D
Problem Solving and Line Plots with Fractional Measurements
Students create line plots from a given set of data. They consider all data points to decide how much of the number line should be shown and how to label the number line to present the data so it can be easily read, analyzed, and understood. Students find the sum of measurements in the data set and use models to equally redistribute the sum among all data points.
Module 3
Multiplication and Division with Fractions
In module 3, students use various strategies to multiply and divide with fractions. They multiply fractions by whole numbers and by fractions, divide whole numbers by unit fractions and unit fractions by whole numbers, and convert customary measurements.
Topic A
Multiplication of a Whole Number by a Fraction
Students extend their understanding of fractions from parts of a whole (e.g., 1 third of a shape) to parts of a set or a number (e.g., 1 third of a group of 12 items). They find fractions of a set and then transition to finding a fraction of a whole number. Students learn that finding a fraction of a whole number means they are finding the product of a fraction and a whole number. They apply this learning to converting customary measurement units.
Topic B
Multiplication of Fractions
Students use area models and number lines to multiply fractions by unit fractions and then fractions by fractions. Throughout the topic, they reason about the value of products by considering whether the factors involved are greater than
1 or less than 1.
TOPIC C
Division with a Unit Fraction and a Whole Number
Students use tape diagrams and number lines to divide a whole number by a unit fraction and to divide a unit fraction by a whole number. They solve word problems that involve multiplication of fractions and division of whole numbers and fractions, and students explain the relationship between multiplication and division.
TOPIC D
Multi-Step Problems with Fractions
Students apply their previous learning about all operations with fractions to compare and evaluate expressions that contain grouping symbols. They create and solve word problems involving fractions, and they write equations with parentheses for word problems that require multiple steps to solve.
Toby spends 2/5 of his money on movie tickets. He spends 1/3
of his remaining money on popcorn. He has $10 left. How much money did Toby have to begin with?
.