Fourth Grade - MATH
5: Math
Unit 5: Fractions
Lesson 1
Basic Fraction Review
Students cut out and rebuild a fraction chart (Activity 2), handling individual fraction pieces that can represent unit fractions and combinations of unit fractions. Students answer questions about how many fourths or twelfths make one whole and color fractions more/less/equal to 1/2, which requires composing and comparing multiple equal parts. Students draw squares and rectangles to show fractions (Wrapping Up) and use an interactive visual fraction tool (Activity 4) that displays fractions as collections of slices.
Lesson 5
Building Fractions
Students use laminated fraction strip pieces to build fractions by placing like-denominator unit fractions end to end (for example, making 3/4 from three 1/4 strips). On Day 2 students are asked to find multiple ways to show one-half using different unit fractions (e.g., 1/4+1/4, three 1/6s, four 1/8s, etc.) and to line up strips with a 1/2 strip to prove equality. The Building Fractions activities require students to match given fractions to different lists of unit fractions and to fill boxes with 1 and unit fractions to create mixed numbers, with answer keys showing decompositions as sequences of unit fractions.
Lesson 6
Adding Fractions
Students are asked to write fractions as sums of unit fractions (e.g., 4/6 = 1/6+1/6+1/6+1/6; 3/4 = 1/4+1/4+1/4) and to produce multiple decompositions (write three ways to make 1 with thirds; come up with four ways to make 1 with fifths). The Student Activity Page explicitly asks students to write three possible equations for given fractions (6/9, 5/11, 7/8). Visual models are provided and used: fraction circles, fraction strips, and a number line are included for students to move pieces or mark points as justification of decompositions.
Lesson 7
Subtracting Fractions
Students use fraction strips to represent 7/8 as seven 1/8 pieces and physically remove five 1/8 pieces to show 7/8 - 5/8 = 2/8, linking the fraction to a sum of unit fractions. A bread/waffle activity has students identify one-sixth parts and combine 1/6 and 2/6 to make 3/6 (recording the equation 1/6 + 2/6 = 3/6) and to subtract 2/6 from 3/6 to get 1/6. Worksheets and boxed problems include explicit equations such as 1/12 + 2/12 and 5/12 + 7/12 that require students to write and match sums of fractions with common denominators.
Lesson 9
Solving Fraction Problems
Students solve and record fraction addition and subtraction equations with like denominators across activities (e.g., 1/2 + 1/4 = 2/4 + 1/4 = 3/4 appears in the answer key). Students add unit-eighths in problems such as 3/8 + 1/8 + 1/8 = 5/8 and use equations in the maze and word-problem pages to follow solution paths. In the Wrapping Up students draw a picture to show 4/4 = 1 and find complementary fractions (for example, 2/10 + 8/10 = 1), recording those sums as equations.
Lesson 10
Adding Mixed Numbers
Students shade circles to represent whole numbers and fractional parts and then combine those shaded models to find sums (Activity 2: Adding Mixed Numbers With Pictures). Students rewrite mixed-number addition as a sum of whole-number and fractional parts using equations (Activity 3 example: 2 2/5 + 3 1/5 = 2 + 3 + 2/5 + 1/5 = 5 + 3/5). Students are instructed to use visual fraction models and to record their work in equations when adding mixed numbers.
Lesson 11
Subtracting Mixed Numbers
Students use visual fraction models (shaded circles) to represent mixed numbers and to show parts being removed during subtraction. The activity and answer key show rewriting wholes as same-denominator fractions for regrouping (e.g., 5 = 4 8/8 and 4 11/8 - 2 6/8) and converting mixed numbers to improper-fraction form during subtraction. Students also perform subtraction by shading and crossing out unit parts in the provided circle diagrams to justify results visually.
Lesson 12
Multiplying Fractions and Whole Numbers
Students draw circles and place unit fraction labels, then write repeated-addition equations such as 1/5+1/5+1/5+1/5=4/5 and 1/9+1/9+1/9+1/9+1/9+1/9=6/9. The materials show equivalences like 3×2/5 = 6×1/5 and 3×3/8 = 9×1/8, and students convert 6/5 into 5/5+1/5 = 1 1/5, using visual models and equations. Answer keys and activities require students to represent multiplication of fractions by whole numbers as sums with like denominators.
Lesson 13
More Practice and Problem Solving
Students are asked in the "What Are the Fractions?" activity to produce multiple number sentences that sum to a target fraction or mixed number (e.g., come up with 3 possible pairs that sum to 7/8, 2 possible triples that sum to 5/4, and 5 possible pairs that sum to 4). Several problems (e.g., the Cupcake problem and many answer-key examples) require students to draw a picture and write an equation showing sums like 1/6 + 3/6 = 4/6 and sample decompositions such as 1/15 + 7/15 or 3/15 + 3/15. Instructions repeatedly direct students to "write number sentences" and "draw a picture" to show their answers, providing opportunities to record decompositions and justify them with visual models.
Lesson 14
Unit Test
Students are asked to write equations that express fractions as sums of like-denominator fractions, for example the answer key includes 1/5 + 1/5 + 1/5 = 3/5. Students complete problems that require adding fractions with the same denominator (e.g., 2/6 + 1/6, 3/4 + 1/4) and they record those sums as equations. The Unit 5 Test Review and Unit 5 Test require students to write equations and simplify fraction sums, which gives practice in expressing fractions as sums with common denominators.
Final Project
Fraction BINGO
Students are instructed to create problems that match given fractions and to create at least three problems that involve adding fractions with the same denominator. Students will place those problems on BINGO cards and then play by matching called fractions to problems on their cards, practicing identification and addition of like-denominator fractions. The materials list and BINGO Problems page list many target fractions (e.g., 6/12, 4/8, 2/3) that students must produce problems for, so students will generate expressions whose answers are those fractions.
Unit 7: Decimals
Lesson 1
Fraction Review
Students are asked to interpret and represent improper fractions as mixed numbers (the lesson directs the child to note that 6/4 is equal to 1 2/4 or 1 1/2 and to draw two fourths-filled wholes and a partially filled one). Students practice generating and writing equivalent fractions and simplifying them (multiple activities require writing fractions in simplest form and matching equivalent fractions). Students also convert fractions to a common denominator to order them (the wrapping-up activity has students write equivalents with denominator 18).
Lesson 6
Decimals on Number Lines and Grids
Students shade grids to show tenths and hundredths (e.g., shading 3 of 10 squares to show 3/10 or 0.3, shading 41/100 by shading one then 40 more), and the lesson explicitly connects 10/100 = 1/10 using the grid model. Students convert between mixed number and decimal notation (e.g., 1.23 = 1 and 23/100) and practice adding fractions with the same denominator (example: 5/12 + 1/12 = 1/2) on the Basic Skills Review. Number-line and grid activities repeatedly ask students to identify and label fractions/decimals and to represent values by shading or marking equivalent parts.
Unit 8: Measurement
Lesson 4
Converting Units of Capacity
Students are asked to draw pictures to solve unit-conversion problems (e.g., drawing eight circles for fluid ounces and two smaller circles in each to count tablespoons) and to use grids that show how a gallon breaks into smaller units (the Illustrating Customary Capacity Units activity and its Challenge to "Draw 2 more grids to make the gallon square break up into smaller units"). The Customary Capacity Conversion Charts and Matching Capacities activities ask students to represent and compare mixed and fractional quantities (e.g., 1/2 pint = 1 cup, 0.5 or 1/2 pint).
Lesson 5
Practice and Problem Solving
Students work with line plots that use fractional measures and count Xs at fractional positions, and they compute totals from those plots (e.g., find the total weight of rabbits that weigh 2 1/4 lb = 6 3/4 lb and the total length of insects measuring 1 1/2 cm = 7.5 cm). The Skills list explicitly states students will "solve problems involving addition and subtraction of fractions by using information presented in line plots." Multiple activities ask students to place Xs at fractional locations and to use those counts to answer additive questions (e.g., Line Plots With Fractions, Measurement Line Plot, Creating a Line Plot).
Unit 9: Skills Review
Lesson 3
Fractions and Decimals
Activity 1 directs students to write addition equations that add up to a given fraction (for example, students are asked to provide decompositions for 4/5 such as 1/5+1/5+1/5+1/5, 2/5+2/5, and 1/5+3/5). The Student Activity Page explicitly instructs students to write three possible equations for each given fraction (examples: 7/9, 6/11, 7/8). The answer key and worksheet examples show recorded decompositions like 1/9+1/9 and other same-denominator sums, indicating students practice recording decompositions as equations.