Fourth Grade - MATH
5: Math
Unit 5: Fractions
Lesson 1
Basic Fraction Review
Students use visual models: they create and partition a square on a geoboard into equal parts and draw fraction diagrams when comparing pizzas. Students cut and rebuild a fraction chart and use an interactive fraction tool that changes slices as numerators and denominators are adjusted. Students identify multiple fractions equal to 1/2 (2/4, 6/12, 3/6, 5/10, 4/8) and answer a prompt noting the numerator is half the denominator.
Lesson 2
Equivalent Fractions
Students use geoboards and shaded fraction bars to show that 2/4, 1/2, and 3/6 represent the same area, and they repeat this with 2/6 vs. 1/3 and 4/6 vs. 2/3. Students are instructed to multiply or divide both numerator and denominator by the same number (example: 3/4 ×3 → 9/12; 10/12 ÷2 → 5/6) and to use an interactive fraction tool to show equal sizes. Multiple activities (fill-in problems, creating equivalent fractions cutouts, domino matching, and worksheets) require students to recognize and generate equivalent fractions by using multiplication/division and matching visual models. The wrap-up asks students to produce several fractions equal to 1/3 and to answer "How do you know?", prompting explanation using models.
Lesson 3
Comparing Fractions
Students play the Equivalent Splat Game where they must click an equivalent fraction and are reminded they must do the same thing to both the numerator and the denominator to find equivalent fractions. Students use fraction chart pieces and a laminated fraction chart to line up and compare fractions (for example 3/6 = 1/2 and 1/2 = 5/10 are given as equalities). Students also use number lines and are asked to draw pictures (e.g., to prove 3/5 < 7/10) which provides visual comparisons of fractions.
Lesson 4
Going Further With Comparing Fractions
Students are asked to produce equivalent fractions (e.g., write two fractions equivalent to 1/3 such as 2/6 and 3/9). The Jess activity explicitly shows converting 2/3 to 10/15 and 3/5 to 9/15 by multiplying numerator and denominator, and practice pages include equations like 2/3 = 6/9 and 10/20 = 20/40. Worksheets and a laminated fraction chart are provided and the Methods for Comparing Fractions sheet includes visual fraction examples to support comparisons.
Lesson 5
Building Fractions
Students use laminated fraction strips to create and align different unit-fraction pieces to show equal lengths (for example, making 1/2 with two 1/4 pieces, three 1/6 pieces, four 1/8 pieces, five 1/10 pieces, or six 1/12 pieces). Students match given fractions to different combinations of unit fractions on the "Building Fractions" sheets and cut-and-place boxes to pair equivalent representations. In the "Building Mixed Numbers Challenge" students show the same mixed number with different sets of strips (for example, 1 2/3 as 1 + two 1/3 strips or 1 + four 1/6 strips).
Lesson 6
Adding Fractions
Students repeatedly use unit fractions to build and represent fractions (e.g., tasks asking students to write 4/6 = 1/6+1/6+1/6+1/6 and similar decompositions). Visual models are used for addition (fraction circles showing 1/4+1/4=2/4) and a number line is shown with sixths marked and a point at 3/6. Students also generate decompositions that make 1 with thirds and fifths, and a Basic Skills item asks students to compare 7/10 and 24/40.
Lesson 7
Subtracting Fractions
The lesson asks students to use fraction strips and number lines (e.g., showing 3/6 = 1/2 and circling the number line that shows 6/8 = 3/4) and to divide a waffle or bread into sixths to name and combine parts. Student pages include fill-in-the-blank equivalence problems such as "5/6 = □/12" and "7/12 = 5/□," and activities that ask students to represent and label equivalent fractions on number lines. The materials direct students to use fraction strip pieces and a laminated fraction chart while ordering and comparing fractional sums and differences, requiring them to recognize and generate equivalent fractions visually.
Lesson 8
Simplifying Fractions
Students are asked to create equivalent fractions by multiplying or dividing both the numerator and the denominator by the same number (example: 3/6 → 1/2, 6/12, 9/18). Students practice recognizing and generating equivalent fractions through step-by-step worksheets (Method #1 and Method #2), matching activities, and multiple practice problems (e.g., simplify 14/28, 4/16, 18/30). Students list factors, find the greatest common factor, and divide numerator and denominator to produce simplified (equivalent) fractions.
Lesson 9
Solving Fraction Problems
Students rewrite and manipulate fractions in several places (for example, the answer 1/2 + 1/4 = 2/4 + 1/4 = 3/4 shows 1/2 represented as 2/4). The practice problems and answer keys include simplifying and recognizing equivalent forms (8/10 simplified to 4/5; 3/9 simplified to 1/3). The Wrapping Up activity asks students to draw a circle divided into four parts and shade all four to show 4/4 = 1, and students use index cards (e.g., 2/10 needs 8/10) to reason about fraction complements with like denominators.
Lesson 10
Adding Mixed Numbers
Students match fractions to pictorial representations and shade circles to show mixed numbers and fractions (Student Activity Page: Different Types of Fractions). The answer key explicitly pairs equivalent fractions such as 3/4 → 6/8 and 1 1/4 → 6/4, showing students examples of equivalent fractions. In the 'Adding Mixed Numbers With Pictures' activity students shade wholes and fractional parts to find sums, using visual models to represent fractions and simplify results.
Lesson 11
Subtracting Mixed Numbers
Students use visual fraction models (shaded circular diagrams) to represent mixed numbers and to perform subtraction by shading and crossing out parts. In the stack-and-regroup examples students rewrite wholes as equal fractional parts to borrow (e.g., 5 = 4 8/8; 6 = 5 4/4), showing they convert a whole into pieces with the same-size denominators. Practice problems ask students to shade circles for fractions like 4 3/6 and 1 2/6 and to simplify answers, reinforcing work with like-denominator fractional parts.
Lesson 12
Multiplying Fractions and Whole Numbers
Students draw circles and place fraction strips or unit-fraction labels in each circle to represent repeated addition (e.g., 4 × 1/5 shown as four 1/5 parts and written as 1/5+1/5+1/5+1/5 = 4/5). The materials include visual answer keys that show repeated-addition visuals for problems like 6 × 1/9 = 6/9 and 3 × 1/5 = 3/5. Some items explicitly show equivalent multiplication expressions (for example, the practice answer key notes 3 × 2/5 = 6 × 1/5 and other equal rewrites) and students are asked to simplify fractions (e.g., 6/9 simplifies to 2/3).
Lesson 13
More Practice and Problem Solving
Students are asked to draw pictures and write equations for fraction problems (e.g., Cooking With Fractions problems explicitly say "Draw a picture and write an equation"). The Introduction shows worked examples where improper/numerator forms are simplified (4/6 simplified to 2/3; 6/8 simplified to 3/4), and answer keys show fractions written with common larger denominators (e.g., 24/4 for 6, lists of twelfths and fifteenths in the "What Are the Fractions?" answers). Several problems include visual aids or number lines to help students represent fractions and sums.
Lesson 14
Unit Test
Students practice recognizing and generating equivalent fractions in the Skills list and Unit Review activities (e.g., problems and answer key showing 2/5 = 8/20, 1/2 = 5/10, 8/12 = 2/3). A linked video titled "Equivalent Fractions" explicitly shows using multiplication and division to create equivalent fractions, and a web game reviews equivalent fractions for additional practice. The Unit 5 Test Review and Unit Test include several items asking students to write missing equivalent fractions, simplify fractions, and identify true/false equivalence statements.
Final Project
Fraction BINGO
The lesson explicitly lists "Recognize and generate equivalent fractions" as a skill and asks students to create problems to match given fractions, including a requirement to create at least three problems for identifying equivalent fractions. The BINGO Caller Cards and BINGO Problems provide many fractions (e.g., 6/12, 4/8, 1/2, 6/10) that students must match with problems, and students place those matching problems on game cards and mark matches during play.
Unit 7: Decimals
Lesson 1
Fraction Review
Students are asked to draw visual models for specific fractions (e.g., draw a circle or rectangle divided into 12 parts with 4 shaded to represent 4/12 and draw two rectangles/circles divided into 4 parts to represent 6/4), which engages use of visual fraction models. Activity 1 and the Student Activity Page require students to recognize and generate equivalent fractions by grouping fractions into suitcase sets and by matching/circling fractions in simplest form (examples shown: 6/12, 1/2, 2/4, 3/6, 10/20 etc.). The Wrapping Up task asks students to write equivalent fractions using a common denominator (e.g., 1/9 = 2/18, 1/6 = 3/18) so students produce equivalents by multiplying numerator and denominator in concrete examples.
Lesson 2
Fractions With Denominators 10 and 100
Students are asked to compare 4/10 and 40/100 and to explain how they are related, prompting them to reason about equivalence. Students complete many conversion problems (e.g., 2/10 = 20/100, ?/10 = 50/100) where they multiply or divide numerator and denominator to generate equivalent fractions. Students use concrete coin examples (3 dimes vs. 3 pennies) and order sets of fractions by converting between denominators 10 and 100. Students change 3/10 to 30/100 when finding sums, applying the equivalence rule in addition.
Lesson 4
Fractions and Decimals
Students practice creating and recognizing equivalent fractions in multiple places: Activity 5 asks them to fill boxes to create equivalent fractions (e.g., problems and answer key showing 2/10 = 20/100, 1/5 = 2/10, 11/20 = 55/100). The Base-10 Fractions and Decimals table and the Converting More Fractions to Decimals exercises have students make equivalent fractions with denominators 10 or 100 and convert them to decimals (explicit Step 1: make an equivalent fraction with denominator 10 or 100). The Fraction-Decimal Match Game requires students to write fraction cards (denominator 10 or 100) and match them to equivalent decimal cards, giving additional practice generating equivalents.
Lesson 5
Mixed Numbers and Decimals
Students convert between decimals and fractions (e.g., 0.7 = 7/10, 0.23 = 23/100, 1.55 = 55/100 or 11/20) and simplify fractions (25/100 to 1/4). Students are asked to draw pictures to represent decimal amounts as fractions (examples show three whole circles and seven-tenth parts for 3.7 and tenths/hundredths visualizations). The materials include examples and practice with tenths and hundredths and matching mixed numbers to decimal/fraction forms.
Lesson 6
Decimals on Number Lines and Grids
Students divide a whole into 10 parts and shade 3 of 10 to show 3/10 (0.3), and then divide the same whole into 100 small squares and shade hundredths (e.g., 41/100, 95/100). The text explicitly directs students to note that a filled row of 10 small squares equals 10/100 and states this is the same as 1/10, and it also points out that 0.2 is the same as 0.20. Number-line activities show the interval 0 to 0.1 broken into ten equal smaller parts (hundredths) so students see how the number and size of parts change while the value stays the same.
Lesson 7
Comparing Decimals
Students use hundredths grid models to shade and compare decimals (e.g., shading 0.32 and 0.29 grids) and write the decimal values of shaded parts. Students compare fractions and decimals in several problems and answers (for example, 8/10 = 0.8, 56/100 compared to 0.4, 4/10 > 0.35, 72/100 < 0.75). Students are instructed to add a zero to a decimal (0.5 → 0.50) to make comparisons easier, showing some connection between different representations.
Lesson 8
Unit Test
Students complete multiple items that generate and recognize equivalent fractions (e.g., fill-in problems such as 8/10 = □/100, 5/10 = 30/100 = □/5, and worksheet answers showing 8/10 = 80/100 and 3/10 = 30/100). Students match fractions to decimals and play matching/concentration games with fraction and decimal cards, reinforcing recognition of equivalent representations. Several comparison and sum problems require converting between denominators 10 and 100 and writing fractions as hundredths.
Final Project
Fraction and Decimal Board Game
Students are instructed to create 20 "Problem!" cards that include 5 problems specifically for creating equivalent fractions with denominators of 10 and 100 (for example, "What's missing? 4/10=?/100"). The Skills list explicitly asks students to "Express a fraction with denominator 10 as an equivalent fraction with denominator 100" and to use that technique when adding fractions with denominators 10 and 100. Students must write answers to each problem card and check them for correctness, providing practice generating equivalent fractions between tenths and hundredths.
Unit 8: Measurement
Lesson 1
Customary and Metric Units
Students complete Basic Skills Review #21 problems that convert and compare fractions and decimals (for example, converting 6/10 to 60/100 and comparing 0.24 with 5/10 and 0.43 with 35/100). Several fraction problems require students to add and simplify fractions (e.g., 5/16 + 3/16 = 1/2) and to multiply a whole number by a fraction (4 × 2/12 = 2/3), giving practice with fractional computation and equivalence in specific cases.
Lesson 4
Converting Units of Capacity
Students draw pictures showing eight fluid-ounce groups with two smaller circles in each to find 16 tablespoons, and they are encouraged to multiply 8 × 2 to get the total. Students complete the "Illustrating Customary Capacity Units" grids that break a gallon into quarts, pints, and cups using shaded square arrays. The materials include fractional expressions in conversions (for example, 0.5 or 1/2 pint = 1 cup and 1/2 L = 500 ml) that connect subdivision of units to fractional notation.
Unit 9: Skills Review
Lesson 3
Fractions and Decimals
Students are asked to write fractions equivalent to 1/2 and to note that they must multiply or divide the numerator and denominator by the same number (examples: 2/4, 5/10, 3/6). The lesson shows generation and recognition of equivalent fractions in examples (2/5 → 4/10, 6/15, 8/20) and groups equal fractions together on comparison cards (e.g., 1/2, 2/4, 5/10). Students also convert fractions to common denominators to compare sizes (3/5 and 4/6 converted to 18/30 and 20/30).