Fourth Grade - MATH
5: Math
Unit 7: Decimals
Lesson 2
Fractions With Denominators 10 and 100
Students convert fractions with denominator 10 to equivalent fractions with denominator 100 (examples: 2/10 = 20/100, 7/10 = 70/100) and complete practice problems that reinforce this skill. Students compare pairs of fractions and record <, >, or = on the activity page (e.g., 5/10 ? 40/100, 30/100 ? 3/10) and order a list of fractions from least to greatest. Students use coin reasoning to compare amounts expressed as fractions of a dollar (e.g., 3/10 as 3 dimes vs 3/100 as 3 pennies).
Lesson 4
Fractions and Decimals
Students read and convert fractions with denominators 10 and 100 to decimals (e.g., 2/10 → 0.2 and 2/100 → 0.02) in the Introduction and Day 2 activities. Students complete Base-10 Fractions and Decimals tables and matching activities that require converting and matching fractions and decimals to the hundredths place. Students answer comparison questions involving money (e.g., Who has more: Carly 45/100 vs Robbie $0.65?) and are asked to "prove who is right" on specific conversion/comparison items (e.g., Sally vs Ted on 3/20).
Lesson 6
Decimals on Number Lines and Grids
Students place and label decimals to tenths and hundredths on number lines in multiple activities (writing 0 and 1 or 1.0 and 2.0 and placing values such as 0.15, 0.51, 0.29, etc.). Students use 10x10 grids to shade hundredths and represent decimals like 0.41, 0.95, and 1.23, connecting decimal notation to visual models. The wrap-up IXL activity directs students to plot two decimal values on a number line and then use the number line to answer a multiple-choice question, which supports reasoning about relative size.
Lesson 7
Comparing Decimals
The lesson explicitly lists the skill "Compare two decimals to hundredths by reasoning about their size" and instructs students to "Record the results of comparisons with the symbols >, =, or <, and justify the conclusions." Students use a number line to justify comparisons of tenths (0.7 vs 0.9) and use hundredths grid models to compare decimals like 0.32 vs 0.29 and 1.08 vs 1.12. The flowchart and practice activities require students to compare whole-number parts first and then compare tenths and hundredths, guiding justification and recording of >, <, or = in multiple exercises.
Lesson 8
Unit Test
Students practice comparing decimals to the hundredths place through spoken prompts, matching and comparison card activities, and several worksheet and test items that ask them to write >, =, or < (e.g., 0.45 □ 0.4, 0.02 □ 0.2, ordering 0.2, 0.24, 0.56, etc.). They are asked to explain their thinking about which number is greater by examining place values left to right and are encouraged to use a laminated number line and visual tools when working. The unit review and test include many problems converting between fractions and decimals and comparing decimals so students repeatedly practice recording comparison symbols and justifying answers.
Final Project
Fraction and Decimal Board Game
The Skills section explicitly tells students to "Compare two decimals to hundredths by reasoning about their size" and to "Record the results of comparisons with the symbols >, =, or <, and justify the conclusions." In Step 4 students create 20 "Problem!" cards that must address comparing decimals (example given: "Which is greater, 0.6 or 0.34?") and then record answers on a provided "Problem! Answers" sheet for checking. The rubric and check procedures require students to provide answers and have them checked for correctness.
Unit 8: Measurement
Lesson 1
Customary and Metric Units
The Basic Skills Review #21 asks students to compare numbers using >, <, or = (Problem 5: compare 0.24 and 5/10; Problem 8: compare 0.43 and 35/100), and Problem 4 has students write 3.56 in expanded form, which addresses place value to the hundredths. The worksheet explicitly directs students to record comparisons with >, <, or = in those problems.
Lesson 2
Converting Units of Length
Students convert between metric units and write measurements using decimals (examples: 0.5 m = 50 cm, 7.5 m from 750 cm, 0.005 km for 5 m) and practice moving the decimal point to change units. Students order eight index cards of different measures from shortest to longest, and complete conversion tables that produce decimal answers (e.g., 40 cm = 0.4 m). The materials include writing whole numbers with a decimal point (1 = 1.0) and exercises that require translating between units that produce decimal representations.
Lesson 4
Converting Units of Capacity
Students convert between liters and milliliters (e.g., 1.5 L = 1500 ml, .25 L = 250 ml) on the "Working With Liters and Milliliters" exercises and complete conversion charts that require changing units before comparing. Students are asked to write capacities in order from least to greatest (2 L, 200 mL, 3000 mL, 1/2 L, 5500 mL, 3.1 L, 1500 mL), which requires comparing values expressed in different units. Several problems (e.g., Marcie vs. Francie; Samuel vs. Marcus) require students to convert to the same unit and then determine who drank more, and some tasks instruct students to draw pictures to answer comparisons.
Lesson 6
Working With Time
Students complete Basic Skills Review items that ask them to place >, <, or = between decimal and fractional values (e.g., 0.74 compared to 5/10 and 0.33 compared to a fraction). Students write a decimal (24.72) in expanded form, which requires understanding place value to the hundredths. Comparison tasks appear as part of the worksheets, so students practice recording comparisons with >, =, or <.
Lesson 8
Working With Perimeter and Area
The Basic Skills Review includes tasks that involve decimals to the hundredths place: students are asked to write 8.07 in expanded form (answer: 8 + 7/100) and to compare values using >, <, or = (examples given: 0.34 compared to 3/10 and 0.46 compared to 5/10). These items require students to record comparison results with the symbols >, =, or <. The presence of decimal notation and comparison items gives students some practice working with decimals and comparison symbols.
Lesson 10
More Practice and Problem Solving
Students are asked to rewrite measurements in the same unit and then place >, =, or < between pairs (Activity 1 and the Student Activity Page), which requires them to compare sizes of quantities. The activity instructions and answer key show students recording comparison symbols for many pairs (e.g., 10 pints > 1 gallon, 5 liters = 5000 ml). The wrap-up prompts require students to explain how they figured answers and which operations they used, allowing students to justify comparisons and to draw pictures as needed.
Lesson 11
Unit Test
Students encounter decimal representations in conversion tables (e.g., 1.14 weeks, 0.032 L) and in measurement amounts (e.g., 1.5 pounds). Students complete comparison tasks for quantities (e.g., "Which is more, 3 yards or 120 inches?" and "Which is more, 1 day or 600 minutes?") that require converting and comparing measures. Students record conversions and answers in tables and fill-in-the-blank items on the Unit 8 Test and review sheets.
Unit 9: Skills Review
Lesson 3
Fractions and Decimals
The Skills list explicitly tells students to "Compare two decimals to hundredths by reasoning about their size" and to "Use decimal notation for fractions with denominators 10 or 100." Activity 2 has students play a Fraction-Decimal Match Game that requires converting between fractions and decimals, reinforcing decimal notation. The Wrapping Up task has students cut out "Review: Ordering Decimals" cards and place given decimals (including examples to the hundredths such as 0.28, 0.35, 0.87, 1.34) in order from least to greatest, which has students compare decimal sizes.
