Fifth Grade - MATH
5: Math
Unit 1: Place Value
Lesson 4
Decimals to Thousandths
Students see multiple explicit examples of decimals to the thousandths with word forms and fraction equivalents (e.g., 0.563 = 563/1000, "five hundred sixty-three thousandths"). Activities ask students to identify tenths, hundredths, and thousandths (circle the digit in place) and to write the value of a digit as a fraction (e.g., 3 in 24.673 = 3/1000). The lesson includes expanded-form and expanded-notation examples and practice (e.g., 1.875 = 1×1 + 8×0.1 + 7×0.01 + 5×0.001 and 2 + 4/10 + 6/100 + 7/1000) and matching/sorting tasks that require students to convert between base-ten numerals, number names, and expanded forms.
Lesson 5
Comparing Decimals
Students write and compare decimals to the thousandths place using a laminated decimal place value chart and decimal grids (examples include 0.152, 0.267, 0.289, 1.358, 1.360, 2.646). Students practice reading and writing decimals in numeral form and reading decimal names aloud in the parent prompts (e.g., asking the child to write five hundred six thousandths and to read 0.378 as "three hundred seventy-eight thousandths"). Activities explicitly ask students to create decimals to the hundredths and thousandths, order them, and explain comparisons using place-value reasoning.
Lesson 6
Rounding to Thousandths
Students are asked to write 3.485 in word form, fraction form, fraction expanded form, and decimal expanded notation on the Unit 1 Quiz 2 page. The answer key shows 3.485 expressed as "three and four hundred eighty-five thousandths," as the fraction 3485/1000, and in expanded notation using 1, 1/10, 1/100, and 1/1000 (e.g., (3 × 1) + (4 × 0.1) + (8 × 0.01) + (5 × 0.001)). Additional items require students to translate expressions like (8 × 1/10) + (3 × 1/100) + (2 × 1/1000) into decimal form (0.832).
Lesson 7
Powers of 10
Students work with decimal place value when they are instructed to have a laminated decimal place value chart and complete the "Powers of 10" sheet that includes problems such as 0.01 × 10 = and 0.1 ÷ 10 =. The parent plan and wrap-up prompt students to say what one-thousandth times 10 equals and to review what happens to decimal numbers when multiplied or divided by 10. The matching activity and answer key explicitly include tenths, hundredths, and thousandths (0.1, 0.01, 0.001) so students practice moving the decimal and recognizing those positions.
Lesson 10
Problem Solving
Students work with a mystery-number answer of 2,971.236 (a decimal to the thousandths place) and must determine that value from clues. The One-Mile Run activity asks students to write times in expanded and word form; the answer key shows decimal expanded form that includes thousandths (7 + 0.8 + 0.002) and a word/fractional expanded example for hundredths (seven and eighty-two hundredths). The Parent Plan Skills explicitly list reading and writing decimals to thousandths and using base-ten numerals, number names, and expanded form.
Lesson 11
Unit Test
The Parent Plan explicitly lists the skill: "Read and write decimals to thousandths using base-ten numerals, number names, and expanded form." Student activities ask learners to fill a place-value table for decimals (e.g., 2.47 and 3.609) with Number Form, Word Form, Fraction Form, and Fraction Expanded Notation. The materials show explicit expanded-form examples using fractional place values (for example, (3 × 1) + (6 × 1/10) + (0 × 1/100) + (9 × 1/1000)) and provide answer-key word-form and fraction examples such as "three and six hundred nine thousandths."
Final Project
Number Trading Cards
The lesson's Skills list explicitly states that students should "Read and write decimals to thousandths" and "Read and write decimals to thousandths using base-ten numerals, number names, and expanded form." The Trading Cards Project requires students to include 4 numbers with decimals (specified to the hundredths place) and asks that each card show the featured number in at least three different forms, including "decimal expanded form." Students are instructed to record numbers and represent them in multiple ways on the Number Collection pages and on the backs of their cards.
Unit 2: Four Operations
Lesson 4
Adding Decimals
Students read a book and answer questions that identify tenths, hundredths, and thousandths (e.g., questions about Tenntts, Hoondrits, and Tousanders) which shows place-value understanding to the thousandths. Students match decimal numerals (for example, 2.26, 1.43) to base-10 block representations, connecting base-ten visuals to written decimals. Students use a decimal place-value chart and practice adding zeros (e.g., 3.4 = 3.40) to align decimals, demonstrating understanding of place-value positions beyond the decimal point.
Lesson 7
Multiplying Decimals
Students represent decimal factors with base-10 drawings (rods = tenths, units = hundredths) and use grids to compute products such as 0.3 × 0.5 = 0.15. Students apply the standard algorithm that counts decimal places and place the decimal in products, producing results with three decimal places in practice problems (e.g., 0.2 × 0.12 = 0.024; 3.8 × 2.32 = 8.816). Students also convert groups of hundredths into tenths (10 hundredths = 1 tenth) when using models.
Unit 3: Measurement
Lesson 1
Reviewing Customary and Metric Units
Students work with decimals in multiple activities: they compute with decimals (multiply 266.3 × 3.9, divide 90 ÷ 2.5, compute 36.6 ÷ 0.3), place several decimal numbers in order (e.g., 2.12, 2.16, 2.09, ...), and round 22.159 to the hundredths place. The Reading Measurements and answer keys include decimal-style measurements (e.g., 8 4/10 cm, 325 ml, 92 g) that require interpreting parts of units and marks between whole numbers.
Lesson 2
Converting Units of Measurement
Students practice moving the decimal point and producing decimal values when converting metric units (e.g., converting 35 meters to 35,000 millimeters and 35 meters to 0.035 kilometers). The curriculum includes arithmetic with decimals in problems such as 4.17 × 3.9, 24 ÷ 2.5, 48.6 ÷ 0.4, and 4.7 × 10^5, which requires reading and writing decimal numerals. The materials explicitly list decimal values like 0.001 kilometers and 0.001 kilograms when describing metric prefixes.
Lesson 4
Working With Time
Students work with decimal quantities of time (examples include 4.7 days, 5.5 minutes, and times given as 8.4, 8.1, 7.8, 7.6, 8.6 hours). Students convert those decimal hours to minutes (e.g., 0.3 hours to 18 minutes) and add decimal totals (e.g., 8.4 + 8.1 + 7.8 + 8.6 = 32.9 hours) to compute minutes. Students compare decimal time values to other units (e.g., comparing 4.7 days to 112 hours).
Lesson 6
Unit Test
Students work with decimal representations when converting units and moving decimal points (for example, 4.5 L = 4,500 mL; 0.45 kg appears in conversion answers; 1.5 km and 0.25 km appear in word problems). The lesson tells students to "think about... moving the decimal the correct number of spaces" when doing metric conversions. The student activity images and answer keys include decimal values (e.g., 0.001 kilometers in the metric chart and 2.3 grams = 2,300 mg) that students must interpret in conversion tasks.
Final Project
Measurement Book
The lesson includes a sample poster titled "Introduction to Decimal Numbers" that displays the decimal 0.25 written as 25/100 and as the number name "twenty-five hundredths," along with a 100-square grid shading to represent 0.25 and a description of the decimal point. That sample is presented in the student/parent pages as an example of how to design an introduction page and to illustrate how decimals can be represented with words, fractions, and visual models.
Unit 9: Skills Review
Lesson 2
Decimal Operations
Students generate and analyze decimal numbers up to thousandths by creating numbers (via the die activity) and answering place-value questions that target tenths, hundredths, thousandths, and ones. The Representing Decimal Numbers table has examples through thousandths showing decimal form, fraction form (e.g., 381/1000), word form (e.g., "three hundred eighty-one thousandths"), and decimal expanded form (e.g., 0.3 + 0.08 + 0.001). The parent notes and introducing directions require students to read decimals aloud in number-name form (example: 1.234 = "one and two hundred thirty-four thousandths") and explicitly list the skill of reading and writing decimals to thousandths in base-ten numerals, number names, and expanded form.
