Students extend their computational work to include fractions and decimals, adding and subtracting numbers in those forms in this unit before moving to multiplication and division in subsequent units.
In the fourth unit for Grade 5, students extend their computational work to include fractions and decimals, adding and subtracting numbers in those forms in this unit before moving to multiplication and division in subsequent units.
Students begin learning about fractions very early. In Grades 1 and 2, students start to explore the idea of a fraction of a shape, visually representing halves, thirds, and fourths (1.G.3, 2.G.3). In Grade 3, they build on this geometric idea of a fraction to develop an understanding of fractions as numbers themselves, using number lines as a representation to make that connection (3.NF.2). Students also start to compare fractions in special cases, including identifying equivalent fractions (3.NF.3). Then, in Grade 4, students extend their understanding of fraction equivalence and comparison, as well as start to operate on fractions. Students also add and subtract fractions with like denominators (4.NF.3) and multiply a fraction by a whole number (4.NF.4), work which they will rely on in this and the next unit.
Thus, Unit 4 starts with a refresher on work in Grade 4, starting with generating equivalent fractions and adding and subtracting fractions with like terms. While students are expected to already have these skills, they help to remind students that one can only add and subtract quantities with like units, as well as remind students of how to regroup with fractions. Then, students move toward adding and subtracting fractions with unlike denominators. They start with computing without regrouping, then progress to regrouping with small mixed numbers between 1 and 2, and then to regrouping with mixed numbers. Throughout this progression, students also progress from using more concrete and visual strategies to find a common denominator, such as constructing area models or number lines, toward more abstract ones like multiplying the two denominators together and using that product as the common denominator (5.NF.1). Then, students use this general method in more advanced contexts, including adding and subtracting more than two fractions, assessing the reasonableness of their answers using estimation and number sense (MP.1), and solving one-, two-, and multi-step word problems (5.NF.2), (MP.4). Then, the unit shifts its focus toward decimals, relying on their work in Grade 4 of adding and subtracting decimal fractions (e.g., $$\frac{3}{10}+\frac{4}{100}=\frac{30}{100}+\frac{4}{100}=\frac{34}{100}$$) and their deep understanding that one can only add like units, including tenths and hundredths as those units, to add and subtract decimals (5.NBT.7). They use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relating the strategy to a written method and explain the reasoning used (MP.1). Students then apply this skill to the context of word problems to close out the unit (MP.4).
As previously mentioned, students will explore the other operations, multiplication and division, of fractions and decimals in Units 5 and 6, including all cases of fraction and decimal multiplication and division of a unit fraction by a whole number and a whole number by a unit fraction (5.NF.3–7, 5.NBT.7). In Grade 6, students encounter the remaining cases of fraction division (6.NS.1) and solidify fluency with all decimal operations (6.NS.3). Students then rely on this operational fluency throughout the remainder of their mathematical careers, from fractional coefficients in functions to the connection between irrational numbers and non-repeating decimals.
Pacing: 18 instructional days (15 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
Additional assessment tools to help you monitor student learning
and identify any skill or knowledge gaps.
Learn how to use these tools with our
Guide to Assessments
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When referred to fractions decimals throughout Units 4--6, use unit language as opposed to “out of” or “point” language (e.g., should be described as “3 fourths” rather than “3 out of 4”). To understand why this is important for fractions (which can be extrapolated to decimals), read the following blog post: Say What You Mean and Mean What You Say by William McCallum on Illustrative Mathematics.
5.NF.A
Find equivalent fractions.
5.NF.A
Add fractions with like denominators.
5.NF.A
Subtract fractions with like denominators.
5.NF.A.1
5.NF.A.2
Add fractions with unlike denominators whose sum is less than 1.
5.NF.A.1
5.NF.A.2
Subtract fractions from fractions less than 1 with unlike denominators.
5.NF.A.1
5.NF.A.2
Add fractions with unlike denominators whose sum is less than 2.
5.NF.A.1
5.NF.A.2
Subtract fractions from fractions less than 2 with unlike denominators.
5.NF.A.1
5.NF.A.2
Add fractions with unlike denominators whose sum is greater than 2.
5.NF.A.1
5.NF.A.2
Subtract fractions from fractions greater than 2 with unlike denominators.
5.NF.A.2
Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.
5.NF.A.1
Add and subtract more than two fractions.
5.NF.A.2
Solve two- and multi-step word problems involving addition and subtraction of fractions.
Key: Major Cluster Supporting Cluster Additional Cluster
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