Fourth Grade - MATH
5: Math
Unit 5: Fractions
Lesson 1
Basic Fraction Review
Students identify numerators and denominators and name fractions (e.g., one-half, three-fourths) when dividing shapes on a geoboard and when writing fractions on the whiteboard. Students cut out and rebuild a fraction chart and use those pieces and an interactive fraction tool that changes the numerator by selecting pieces, which lets them manipulate and count unit parts. Students draw and shade shapes to show specific fractions (for example 3/6, 3/9, 2/8, 5/8) and answer questions about how many fourths or twelfths make a whole.
Lesson 2
Equivalent Fractions
Students use geoboards and shaded bars/grids to show that fractions with different numerators and denominators (e.g., 2/4, 1/2, 3/6; 2/6 and 1/3; 4/6 and 2/3) represent the same amount. Students practice creating equivalent fractions by multiplying or dividing numerator and denominator (e.g., 3/4 multiplied by 3 to get 9/12; 10/12 divided by 2 to get 5/6). In the wrap-up students write multiple fractions equal to 1/3 (2/6, 3/9, 4/12), reinforcing the idea of repeated equal-sized parts.
Lesson 3
Comparing Fractions
Students mark fractions on number lines (including improper fractions such as 5/4) and use fraction-chart pieces to line up and compare unit fractions (for example, comparing 1/3 to 1/2). Students are asked to explain why 6/8 is bigger than 3/8 by noting that both are made of eighths and that 6 parts of 1/8 is more than 3 parts of 1/8. The lesson has activities that repeatedly ask students to work with and compare single-piece fractions (1/b) as benchmarks.
Lesson 4
Going Further With Comparing Fractions
Students work with a section titled "Comparing Fractions With a Numerator of 1," where they compare unit fractions (e.g., 1/2 vs 1/12) and reason about how larger denominators make smaller unit fractions. Students convert fractions by multiplying numerator and denominator (for example, converting 2/3 to 10/15 and 3/5 to 9/15) when they list multiples and create equivalent fractions. Students use a laminated fraction chart, index cards of fractions, and practice ordering fractions from least to greatest, which encourages thinking about fractions in terms of unit pieces.
Lesson 5
Building Fractions
The Skills section explicitly states students should "understand a fraction a/b with a > 1 as a sum of fractions 1/b." In the Introduction students place like-denominator strips end to end to make fractions (e.g., make 3/4 by placing three 1/4 pieces). Day 2 activities ask students to find many ways to make 1/2 using unit fractions and to match given fractions with different ways to make them using unit fractions. The Building Mixed Numbers Challenge has students create mixed numbers by combining wholes and unit-fraction strips (e.g., show 1 2/3 as one whole + two 1/3 strips or as one whole + four 1/6 strips).
Lesson 6
Adding Fractions
Students are prompted 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; 2/5 = 1/5+1/5). Visual models and a number line are used to show unit-fraction increments (dots at 0/6, 1/6, 2/6, etc.), and fraction-circle images illustrate sums like 1/4+1/4=2/4. Activity 2 has students compose 1 using unit fractions (1/3+1/3+1/3; 1/3+2/3; and various ways with fifths), and the student pages ask for multiple equations for given fractions (e.g., three equations for 6/9, 5/11, 7/8).
Lesson 7
Subtracting Fractions
Students use fraction strip pieces to show 7/8 as seven 1/8 strips and remove five 1/8 strips to get 2/8, so they represent fractions by counting unit fractions. The lesson has students divide a bread/waffle into six equal parts, name one-sixth, identify two-sixths and three-sixths, and model adding and subtracting those sixths. The interactive tool and worksheets require students to change numerators while keeping like denominators, encouraging visualization of a fraction as a number of 1/b pieces.
Lesson 9
Solving Fraction Problems
Students are asked to draw and explain that 4/4 equals 1 and to shade a circle divided into four parts, which provides a visual model of unit fractions. Several solved equations and examples (for example, 1/2 + 1/4 = 2/4 + 1/4 = 3/4) show students composing fractions with like denominators and rewriting fractions as sums of equal unit pieces. The index-card activity asks students to name the fraction needed to add to a given fraction to make 1 (e.g., for 2/10 add 8/10), which has students reason about parts with the same denominator and complements to a whole.
Lesson 10
Adding Mixed Numbers
Students draw and analyze pictures of fractions in Activity 1 where the teacher may write 4/3 and draw circles divided into thirds to show it is more than 1, and students complete the "Different Types of Fractions" sheet that matches mixed numbers to improper fractions (e.g., mapping mixed-number pictorials to forms like 1 1/4 → 6/4). In Activity 2 and the adding-with-pictures page, students shade whole circles and fractional parts separately, combining shaded unit parts to find sums. The Adding More Mixed Numbers example explicitly decomposes mixed-number addition as 2 + 3 + 2/5 + 1/5 = 5 + 3/5, showing students break fractions into like unit-fraction pieces.
Lesson 11
Subtracting Mixed Numbers
Students shade and mark circle diagrams to represent mixed numbers and their fractional parts (e.g., shading 4 3/6 and marking Xs for 1 2/6) and use those visual models to perform subtraction. Answer-key examples and worked problems show converting wholes into equal fractional parts (e.g., 5 = 4 8/8, 6 = 5 4/4) when regrouping, which represents wholes as sums of unit fractions. The activities ask students to verify results with addition and to use pictured fractional units in subtraction tasks.
Lesson 12
Multiplying Fractions and Whole Numbers
Students draw fraction-strip and circle models for problems like 4 × 1/5, 5 × 1/8, and 6 × 1/4 and place unit fractions in each group. They write repeated-addition sentences (e.g., 1/5+1/5+1/5+1/5 = 4/5) and record multiplication equations (e.g., 6 × 1/4 = 6/4). A student example box explicitly shows 5 × 1/4 with a visual and the activity prompts converting improper fractions to mixed numbers (e.g., 6/5 → 1 1/5).
Lesson 13
More Practice and Problem Solving
Students set up and solve problems that multiply whole numbers by unit fractions (for example, the whiteboard examples 4 × 1/4 and the wrap-up items 8 × 1/4, 3 × 1/3, 5 × 1/3). The Day 2 prompt has students compute 5 batches × 2/3 cups and allows repeated addition or multiplication, and the teacher script models setting up 3 × 1/2 to find 3/2. The answer keys include computations written as improper fractions from whole×unit-fraction contexts (e.g., 9 batches × 1/8 = 9/8 or 1 1/8).
Lesson 14
Unit Test
Students are asked to compute products of whole numbers and fractions in the 'Find the products' section (e.g., 3 x 1/2, 5 x 1/5, 7 x 1/7) and to write equations and answers for these problems. The answer keys and practice items include examples of multiplying whole numbers by unit fractions and non-unit fractions (e.g., 3 x 1/4 = 3/4, 5 x 2/3 = 10/3, 3/4 x 7 = 21/4). The Unit Test instructions tell students to 'Draw pictures and write equations to solve the problems,' which gives students opportunities to represent fraction multiplication pictorially for word problems.
Final Project
Fraction BINGO
Students are asked to create problems that match given fractions and to create at least three problems that involve multiplying a fraction by a whole number (BINGO Problems page). The BINGO Caller Cards include target fractions (including improper fractions like 5/4) that students must match to problems they write. Step 6 instructs students to teach other players the required skills, including multiplying a fraction by a whole number, and allows use of a whiteboard to explain solutions.
Unit 7: Decimals
Lesson 1
Fraction Review
Students are asked to draw visual models for fractions such as 4/12 and 6/4, including drawing circles or rectangles divided into equal parts and shading the appropriate number of parts. Students decompose an improper fraction (6/4) into a whole and a fractional part, recognizing it as 1 2/4 or 1 1/2. Students practice equivalent fractions and rewrite fractions with a common denominator (e.g., converting several fractions to eighteenthths) when ordering fractions from least to greatest.
Lesson 3
Decimal Place Value
Students convert decimal digits to fractions (for example, the sheet shows 2.37 broken down into 3/10 and 7/100 and asks for values like 6 in 24.67 = 6/10). Students write decimals in expanded form using multiplication by place-value units (examples show 623.5 = (6×100)+(2×10)+(3×1)+(5×0.1) and other numbers decomposed into sums and products). Matching activities connect decimals such as 0.2, 0.05, and 0.36 to names like two-tenths and five-hundredths, reinforcing the idea that digits represent fractional parts.
Lesson 5
Mixed Numbers and Decimals
Students convert between decimals and fractions (for example, 0.7 → 7/10 and 0.23 → 23/100) and practice reading fractions in unit-fraction language ("one and seven-tenths"). Students draw visual models that show whole units plus parts (e.g., three whole circles and seven-tenth parts to represent 3.7) and represent mixed numbers such as 2 8/10 as 2.8, noting that 8/10 corresponds to the decimal .8. The materials ask students to show decimal amounts with shapes divided into tenths or hundredths, reinforcing the idea of parts of a whole.
Lesson 6
Decimals on Number Lines and Grids
Students shade grids to show parts of a whole and are asked to name those shaded parts as fractions and decimals (for example, shading 3 of 10 sections and writing 3/10 or 0.3). The lesson has students shade 41/100 and 95/100, and it points out that a full row of ten hundredths is 10/100 = 1/10. Number-line activities ask students to label tenths and hundredths and to locate decimals such as 0.15, 0.51, and 3.04, reinforcing the idea of counting unit parts (tenths or hundredths).
Unit 8: Measurement
Lesson 1
Customary and Metric Units
The Basic Skills Review #21 includes fraction problems such as solving and simplifying 4 × (2/12) and adding fractions (5/16 + 3/16), and other items work with fraction–decimal relationships (x/10 = 60/100, expanded form of 3.56). These items require students to compute with fractions and to multiply a whole number by a fraction in written form.
Lesson 4
Converting Units of Capacity
Students draw visual groupings and use multiplication to find equivalent quantities (e.g., drawing eight fluid-ounce circles with two tablespoons in each and computing 8 × 2 = 16). The Working With Liters and Milliliters materials present unit-fraction conversions such as 1/2 L = 500 mL and .25 L = 250 mL and include mixed-number-to-milliliter conversions (e.g., 3 L 800 mL = 3800 mL, 1.5 L 200 mL = 1700 mL). The illustrating-customary-units grids ask students to break larger units into equal smaller-unit grids, supporting partitioning and counting of equal parts.
Lesson 5
Practice and Problem Solving
Student tasks require totaling repeated fractional measurements from line plots (for example, the Creating a Line Plot answer shows students finding the total weight of rabbits that weigh 2 1/4 pounds as 6 3/4, which is 3 × 2 1/4). The Measurement Line Plot answers include computing total length for measurements listed multiple times (e.g., total length of insects measuring 1.5 cm = 7.5 cm), which reflects multiplying a fractional measurement by a count. The Line Plots With Fractions activities ask students to place Xs for repeated unit fractions (1/4, 3/4, etc.) and answer questions based on counts of those fractions.
Unit 9: Skills Review
Lesson 3
Fractions and Decimals
The Adding and Subtracting Fractions activity asks students to produce addition equations that add up to a given fraction (e.g., for 4/5 students give 1/5+1/5+1/5+1/5 or 2/5+2/5), and the Equation Writing section asks students to write multiple equations for given fractions. The example prompts and answer key show students composing fractions as sums of unit fractions (repeated 1/b parts).