Curriculum for Grade 5
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MODULE 1. Place Value and Decimal Fractions
Topic A: Multiplicative Patterns on the Place Value Chart
Relying on solid understanding of the place value chart and powers of ten, students multiply and divide to solve problems with a decimal number as a factor or quotient.
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Topic B: Decimal Fractions and Place Value Patterns
Students use familiar symbols (<, =, >) to compare numbers to the thousandths place. They identify, compose, and arrange numbers of equal and unequal length.
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Topic C: Place Value and Rounding Decimals
Students review the place value of decimal numbers. They use the basic algorithm for rounding whole numbers to round decimals to the ones, tenths, and hundredths place.
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Topic D: Adding and Subtracting Decimals
Based on the familiar disk model, students add and subtract numbers to the thousands place. They add and subtract in equations that require regrouping and learn to use the standard algorithm (column addition and column subtraction).
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Topic E: Multiplying Decimals
Students take the first steps in understanding multiplication of a decimal number. Working with a single-digit whole number and a decimal number, students work step-by-step through the process using the familiar disk model. They trade disks to model regrouping and explore the importance of decimal point placement.
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Topic F: Dividing Decimals
Students rely on familiar models and procedures to apply their division knowledge to decimals. Step-by-step, they learn to correctly work through regrouping, using a new place value, using zeros, and placing a decimal in their quotient.
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MODULE 2. Multi-Digit Whole Number and Decimal Fraction Operations
Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication
Students work with round numbers in the tens, hundreds, and thousands to see how factoring out can make mental multiplication easier. In doing so, they apply properties of multiplication.
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Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication
Students hone their use of the standard algorithm for multiplication, working with multi-digit numbers. They master the use of regrouping and working across zeros. To further their conceptual understanding, the standard algorithm is presented alongside other strategies, such as the area model and factoring out powers of 10.
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Topic C: Multiplying with Decimals and Multi-Digit Numbers
Students begin to multiply decimals in the tenths or hundredths by 2- or 3-digit whole numbers. They learn how to accurately place a decimal in their answer and how to estimate to check the reasonableness of their answer.
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Topic D: Mental Strategies for Multi-Digit Whole Number Division
Students rely on their understanding of powers of 10, division, place value, and rounding to divide multi-digit whole numbers mentally.
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Topic E: Partial Quotients and Multi-Digit Whole Number Division
Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.
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Topic F: Partial Quotients and Multi-Digit Decimal Division
Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.
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MODULE 3. Addition and Subtraction of Fractions
Topic A: Equivalent Fractions
Students are introduced to the basics of fraction equivalency. They learn to multiply to find an equivalent fraction and to divide to reduce a fraction. The concepts of common factors and greatest common factor are also introduced and applied.
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Topic B: Making Like Units Pictorially
Students rely on their knowledge of fraction equivalence to work through all aspects of adding and subtracting with fractions and mixed numbers. With plenty of visual support and step-by-step prompting, they work with like and unlike denominators. Students learn to convert between mixed numbers and fractions to solve problems, write their answer in simplest form, and solve word problems.
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Topic C: Making Like Units Numerically
Students increase the complexity of the addition and subtraction operations they can solve by using mixed numbers. They reinforce and apply their understanding of number equivalence as they rename numbers to solve problems.
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Topic D: Further Applications
To support more complex understanding of operations with fractions, students are supported by visual models, the number line, and diagrams. They apply their knowledge of fractions to estimate sums and differences and solve multi-step word problems with mixed numbers.
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MODULE 4. Multiplication and Division of Fractions and Decimal Fractions
Topic A: Line Plots of Fraction Measurements
Students combine their knowledge of measurement, rounding, and mixed numbers to create line plots. They then analyze the data, requiring them to perform operations with mixed numbers.
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Topic B: Fractions as Division
To solidify their understanding of fractions as division, students work to convert between the two, using fractions greater than and less than one. They then work step by step to make sense of the remainder of a division problem as a fraction. Equipped with this understanding, students solve increasingly complex division word problems.
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Topic C: Multiplication of a Whole Number by a Fraction
Students begin by finding a unit fraction of a whole number and other fractions of a whole number using familiar models. They then relate that process to multiplication. To multiply a whole number by a fraction, students learn to find common factors and reduce either before or after multiplying.
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Topic D: Fraction Expressions and Word Problems
Students synthesize their understanding of fractions and operations to build and solve expressions. Familiar models support their learning, and word problems put the skills in context.
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Topic E: Multiplication of a Fraction by a Fraction
Students learn to multiply fractions by starting with unit fractions and the support of an area model. They then progress to multiplication that involves mixed numbers, reducing, and units of measure.
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Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems
Students explore the effects of multiplying by less than, equal to, and greater than 1. They solve multiplication problems, provide missing factors, and complete inequalities to solidify their understanding.
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Topic G: Division of Fractions and Decimal Fractions
Students rely upon their understanding of multiplying fractions to learn how to divide fractions. With the assistance of familiar models such as tape diagrams and area models, they learn different ways to approach dividing with fractions. At this stage, they use unit fractions with whole numbers and unit fractions with unit fractions.
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MODULE 5: Algebraic Expressions
Topic A: Solving Complex Missing Addend Equations
Students solve increasingly complex missing addend equations. In these pre-algebra equations, the challenge is not in the number values but in the logic of how numbers and equations can be combined to solve for numbers represented by symbols.
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