HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 5

Unit 5: Fractions

Students work with fractions that include denominators of 10 in multiple activities (examples: 6/10, 7/10, 5/10 appear in the "More, Less, and Equal" activity and the "Who Ate More?" problems). Students compare and reason about tenths when deciding which fraction is larger or equal (e.g., recognizing 5/10 = 1/2). The fraction chart and cut-and-rebuild activities include a variety of denominators including tenths, so students practice naming and comparing fractions with denominator 10.
Unit 7

Unit 7: Decimals

Students convert between tenths and hundredths in multiple activities (e.g., problems showing 2/10 = 20/100, 7/10 = 70/100, and 90/100 = 9/10). Students use coin contexts to compare fractions (e.g., reasoning that 3/10 = 30/100 by thinking of dimes vs. pennies). Students change a fraction with denominator 10 to an equivalent fraction with denominator 100 to add fractions (e.g., rewriting 3/10 as 30/100 to add to 15/100 and get 45/100).
Students match decimal numbers to their word names (for example, 0.36 to "thirty-six hundredths") and identify digits in the tenths and hundredths places. Students break decimals into fractional parts in expanded form (examples include 2.37 shown as 3/10 and 7/100, and 5.62 shown as 5 + 0.6 + 0.02). Students answer value-of-digit questions using fractional notation (for example, the value of 5 in 37.57 is given as 5/10).
The lesson explicitly lists the skill "Use decimal notation for fractions with denominators 10 or 100" and has early practice converting 2/10 to 0.2 and 2/100 to 0.02. Multiple activities require students to convert between fractions and decimals (Base-10 Fractions table, Converting More Fractions to Decimals, matching games) and to write decimal equivalents for coin amounts (e.g., 63/100 = $0.63, $0.56, $0.77). Tasks ask students to rewrite decimals as fractions (Jane ran .55 mile -> 55/100) and to create matching fraction–decimal pairs, giving repeated practice with denominators 10 and 100.
Students convert between decimals and fractions in multiple places (for example, writing 0.7 as 7/10, 0.23 as 23/100, and 1.55 as 55/100) and simplify conversions (e.g., 55/100 to 11/20). Students convert mixed numbers with tenths and hundredths to decimals (e.g., 6 45/100 to 6.45, 3 62/100 to 3.62, and 2 8/10 to 2.8) and read their word forms aloud. Students draw visual representations of decimals (e.g., drawing shapes to show 2.3, 3.7, and 1.9) and complete matching and table activities that pair mixed numbers with their decimal equivalents.
Students convert between fractions with denominators 10 and 100 and decimal notation by shading grids and writing both forms (e.g., shading 3/10 and identifying it as 0.3, shading 41/100 and identifying it as 0.41, and writing 1.23 as 1 23/100). Students label tenths and hundredths on number lines and locate specific decimals (e.g., 0.15, 0.51, 0.29, 0.75, 0.81) through guided practice and interactive games. Worksheet activities require students to match decimal values to points on number lines and to fill or interpret grids as hundredths, reinforcing the connection between fractions (tenths/hundredths) and decimal notation.
Students place and compare decimals on a number line by labeling 0 to 1 and marking tenths (e.g., comparing 0.7 and 0.9). Students use hundredths grids to color shaded parts and write their decimal values (e.g., shading to produce 0.32, 1.08, 1.12). Students compare fractions and decimals and are given and asked to use equivalences such as 8/10 = 0.8, 56/100 and 0.4, and 72/100 < 0.75.
The Skills list explicitly states: "Use decimal notation for fractions with denominators 10 or 100." Student activities require converting between 10ths/100ths and decimals (e.g., 8/10 = 80/100, 56/100 = 0.56, and converting 7 + 6/10 + 2/100 to 7.62). Multiple pages ask students to match fractions and decimals, compare fractions and decimals (e.g., 3/10 vs 0.4, 0.07 vs 0.7), and write decimals in expanded form. Students are encouraged to use a laminated number line and are given a web link to an interactive "Decimals on the Number Line" activity, supporting placement of decimals on a number line.
The Skills list explicitly includes "Use decimal notation for fractions with denominators 10 or 100." The Problem! card instructions require students to create 5 cards that "identify equivalent base-10 fractions and decimals (for example, 'What decimal is the same as 43/100?')." Students must write and check answers for these Problem! cards on the provided answer sheets, practicing conversion between fractions (denominators 10 and 100) and decimals.
Unit 8

Unit 8: Measurement

The Basic Skills Review #21 asks students to write 3.56 in expanded form as 3 + 5/10 + 6/100, showing how decimal place values relate to tenths and hundredths. The same review includes items that compare decimals and fractions (e.g., compare 0.24 with 5/10 and 0.43 with 35/100) and converts 6/10 to 60/100, giving practice with equivalent hundredths and decimal notation. The metric conversion guidance also tells students they can use moving the decimal point (e.g., change 1 to 1.0 and shift decimals) when converting metric units, reinforcing decimal place value.
Students convert metric measurements into decimal notation for lengths in multiple places (for example, students convert 40 cm to 0.4 m, 750 cm to 7.5 m, and 5 m to 0.005 km). The materials explicitly include decimal expressions such as 0.5 m and remind students that whole numbers can be written with decimal points (1 = 1.0). Students practice moving the decimal point when converting between metric units.
Students write decimal equivalents when converting metric weights (for example, they write 1 gram = 0.001 kilograms and 300 grams = 0.3 kilograms in the answer key and activities). Students complete a metric flip chart and use the 'King Henry Died By Drinking Chocolate Milk' chart to record and check equivalent metric measures using decimal notation. Several practice problems require students to produce decimal kilogram values from gram quantities (e.g., 25 kilograms = 25,000 grams and 300 grams = 0.3 kilograms).
Students work with decimal liters in metric conversions (examples include 2.5 L = 2500 ml, 3.1 L in ordering tasks, and .25 L = 250 ml shown in the matching answers). The "Working With Liters and Milliliters" exercises and the matching activity present decimals for capacities and have students convert those decimal liter values to milliliters. The ordering and fill-in-the-blank tasks require students to read and use decimal representations of liters alongside milliliter amounts.
Students convert measures that result in decimal answers (for example, Kelly walking 500 m/day for a week gives the answer 3.5 kilometers). Students read and interpret line plots that use decimal measurements (the insect plot lists 1.5 cm and 4.5 cm) and place/locate measurement values on number-line style plots. Several activities require students to label answers with measurement units and to work with tenths (e.g., 3.5 km) when solving conversion problems.
Several items require students to work explicitly with tenths and hundredths: Basic Skills Review #22 asks students to write 24.72 in expanded form as 20 + 4 + 7/10 + 2/100. The same review includes comparison items that pair decimals and fractions (0.74 > 5/10 and 0.33 > 3/10) and a fraction addition that produces hundredths (3/100 + 6/10 = 63/100). These tasks show students interpreting decimal places and comparing decimals with fractions having denominators 10 or 100.
Students work with decimals and hundredths on the Basic Skills Review: they write 8.07 in expanded form as 8 + 7/100, they compare 0.34 to 3/10, and they compute 5/100 + 2/10 = 25/100. The review also includes comparing 0.46 to 5/10, which requires students to relate a decimal to a fraction with denominator 10.
Students are asked to work with metric conversions and shown that the metric system is based on 10 (question: "What number is the metric system based on? (10)"). Student activity items require comparing 5000 ml and 5 liters and include equivalents such as "5 liters = 5000 ml". The answer key also uses a decimal in a comparison ("0.5 liters < 5000 milliliters"), indicating students will encounter decimal notation for a tenth in the context of units.
Unit 9

Unit 9: Skills Review

The lesson's Skills list explicitly includes "Use decimal notation for fractions with denominators 10 or 100." Activity 2 directs students to re-watch a video titled "Converting Base-10 Fractions" and to play a "Fraction-Decimal Match Game" where they turn over cards to find matching fraction/decimal pairs. The Wrapping Up activity has students order decimal cards (e.g., 0.01, 0.1, 0.2, 0.28) from least to greatest, giving practice reading and comparing decimals to the hundredths place.