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.
Math
Unit 4
5th Grade
In the fourth unit of 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. 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 how to regroup units (i.e., wholes). 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 conclude 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)
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The following assessments accompany Unit 4.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 7.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
area model |
Example: Use an area model to solve $$\frac{1}{2}+\frac{1}{3}$$. |
tape diagram |
Example: Use a tape diagram to solve $$\frac{1}{4}+\frac{1}{8}$$. |
number line |
Example: Use a number line to solve $$\frac{2}{3}-\frac{2}{9}$$. |
Word Problems and Fluency Activities
Access daily word problem practice and our content-aligned fluency activities created to help students strengthen their application and fluency skills.
Topic A: Addition and Subtraction of Fractions
Topic B: Addition and Subtraction of Decimals
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 3
Shapes and Volume
Unit 5
Multiplication and Division of Fractions