HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 5

Unit 5: Fractions

Students encounter explicit examples converting between denominators 10 and 100: the Finding Equivalent Fractions answer key shows 50/100 = 5/10, and the Creating Equivalent Fractions answer key shows 40/100 = 4/10. Several student activity pages and examples include fractions with denominator 10 (e.g., 2/10 = □/5 and 4/10 = 2/5), and teacher prompts emphasize multiplying/dividing numerator and denominator to create equivalent fractions. Activities require students to generate and match equivalent fractions (cut-and-paste, dominoes, fill-in-the-blanks) including cases involving 10 and 100 as denominators.
Students play an Equivalent Splat Game where they must click an equivalent fraction and are reminded that they must do the same thing to both numerator and denominator to find an equivalent fraction. Several activities and answer keys show and use fractions with denominator 10 (for example, number-line tasks with 3/10 and 8/10 and the answer 1/2 = 5/10). Students mark and compare fractions on number lines and write <, >, or = between pairs that include tenths (e.g., 5/10) so they practice recognizing equivalent tenths and comparing them to other fractions.
Students practice creating equivalent fractions by multiplying numerator and denominator (for example, converting 2/3 to 10/15 and 3/5 to 9/15 on the Jess worksheet). The materials include other explicit scaling examples (2/3 = 6/9, 10/20 = 20/40) and directions to find common multiples to make denominators the same. Students use these equivalent-fraction skills to compare and order fractions (e.g., ordering 3/10, 11/30, 1/2, 12/15, 5/6).
Students are asked to recognize and generate equivalent fractions (listed under Skills) and are directed to a video that "shows how we use multiplication and division to create equivalent fractions." The answer keys include examples of converting and simplifying (e.g., 5/10 = 10/20, 1/2 = 5/10) and include addition/subtraction problems with tenths (e.g., 4/10 + 3/10 = 7/10; 7/10 - 3/10 = 4/10). The student tasks require students to simplify fractions and add/subtract fractions with like denominators, including denominators of 10 in mixed-number contexts (e.g., 6 7/10 - 2 4/10).
Unit 7

Unit 7: Decimals

Students practice recognizing and generating equivalent fractions by sorting fractions into groups on the "Equivalent Fractions Review" activity (suitcases and socks), where fractions such as 3/10 and 50/100 appear among the items to be matched. Students practice adding and subtracting fractions with like denominators on the "Adding and Subtracting Fractions Review" sheet, and students are prompted in the Wrap Up to write equivalent fractions with a common denominator (all converted to 18) to order fractions.
The Facts and Definitions and Skills sections explicitly instruct students to change a fraction with denominator 10 to an equivalent fraction with denominator 100 and then add numerators. Activity 1 and its student page provide direct practice converting examples (e.g., 2/10 = 20/100, 7/10 = 70/100, ?/10 = 50/100). Activity 3 and its worksheet show and require students to convert a 10-denominator fraction to 100 (e.g., 3/10 -> 30/100) and then add with a fraction over 100, with multiple worked examples and an answer key (e.g., 3/10 + 15/100 = 45/100).
Students break decimals into tenths and hundredths (example: 2.37 is shown as 3/10 and 7/100) and match decimals to their verbal names (e.g., 0.05 as five-hundredths, 0.36 as thirty-six hundredths). Several problems ask for the value of a digit in fractional form (for example, the value of 6 in 24.67 is given as 6/10 and the value of 5 in 37.57 is given as 5/10). Expanded-form exercises represent decimal digits using fractional values (examples like 5.62 = 5 + 0.6 + 0.02 and other decimals shown in fraction form).
Students are asked to create and record equivalent fractions with denominators 10 and 100 (e.g., Activity 5 answer key shows 2/10 = 20/100 and the Base-10 Fractions table includes 3/10 → 0.3 and other tenths and hundredths examples). The Fraction-Decimal Match Game instructs students to write fractions with a denominator of 10 or 100 and match them to equivalent decimals. Several conversion activities and practice sheets require students to make equivalent fractions with denominator 100 (e.g., 11/20 = 55/100, 8/25 = 32/100) and then write the decimal form.
The lesson explicitly asks students to use decimal notation for fractions with denominators 10 or 100 and has multiple tasks converting between decimals and fractions (e.g., 0.7 → 7/10, 0.23 → 23/100, 4.56 → 4 56/100). Students practice writing mixed numbers as decimals (e.g., 2 8/10 = 2.8, 6 45/100 = 6.45) and converting decimal place values into hundredths (examples show 56/100 for .56). The lesson also has students simplify hundredths (e.g., simplifying 25/100 to 1/4), showing work with both tenths and hundredths place values.
Students practice representing tenths and hundredths using grids and number lines: they shade three tenths (3/10 or 0.3) on a tenths grid and shade hundredths squares to show values like 0.41 (41/100). The text explicitly states and has students observe that a filled row equals ten-hundredths, 10/100, and that 10/100 is the same as one tenth, 1/10 or 0.1. Activities ask students to convert between fraction and decimal forms for tenths and hundredths (e.g., shading 21/100 and writing 0.21, and labeling tenths as 0.1, 0.2, etc.).
The lesson's Skills list explicitly states the target skill: "Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100." Student activity and test items require conversions (e.g., 8/10 = 80/100; 3/10 = 30/100) and direct addition of tenths and hundredths (e.g., 2/10 + 35/100 = 55/100; 6/10 + 26/100 = 86/100). Multiple student pages include fill-in-the-blank and sum problems (for example, 7/100 + 1/10, 12/100 + 7/10) that have students practice converting 10ths to 100ths and then adding.
Students are asked to practice the skill explicitly listed in the Skills section: "Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100." In Step 4 students create 5 "Problem!" cards that ask for creating equivalent fractions with denominators 10 and 100 (example: "What's missing? 4/10=?/100") and 5 cards that ask for adding fractions with denominators 10 and 100 (example: "Find the sum: 30/100+2/10"). Students write answers on a provided answer sheet and have their answers checked for correctness.
Unit 8

Unit 8: Measurement

Students complete Basic Skills Review #21 which includes converting a fraction with denominator 10 to an equivalent fraction with denominator 100 (the answer key shows 6/10 = 60/100). Students also write a decimal in expanded form (3.56 = 3 + 5/10 + 6/100), so they represent tenths and hundredths side by side. These tasks require students to recognize and produce equivalent tenths-to-hundredths representations.
The Basic Skills Review answer key shows the addition 3/100 + 6/10 = 63/100, demonstrating an instance of adding a fraction with denominator 10 to a fraction with denominator 100. The expanded-form item for 24.72 is written as 20 + 4 + 7/10 + 2/100, which links tenths and hundredths as related units. Additional items compare decimals and fractions (for example 0.74 > 5/10), reinforcing understanding of tenths vs. hundredths.
Students are asked to solve Basic Skills Review item 7, which is 5/100 + 2/10 = ? with the answer key showing 25/100. The Basic Skills Review also includes writing 8.07 in expanded form (8 + 7/100) and a comparison item showing 0.34 > 3/10, which involves reasoning about hundredths and tenths. These items require students to work with hundredths and to combine fractions/decimals with denominators 10 and 100.
Unit 9

Unit 9: Skills Review

Students are asked to generate equivalent fractions and are shown how to multiply or divide the numerator and denominator by the same number (Introduction examples such as 1/2 -> 5/10 and 2/5 -> 4/10). The Skills list explicitly includes "Use decimal notation for fractions with denominators 10 or 100." Activity 2 directs students to review converting fractions to decimals (a linked video titled "Converting Base-10 Fractions") and to play a Fraction-Decimal Match Game and order decimals to the hundredths place.