Fifth Grade - MATH
5: Math
Unit 1: Place Value
Lesson 4
Decimals to Thousandths
Students use laminated decimal grids to represent and compare values such as 0.6 and 0.06 and are prompted to notice that 0.6 is much greater than 0.06. Students complete place-value tasks that ask them to circle digits in the tenths, hundredths, and thousandths places and to write the value of specific digits as fractions (for example, identifying the 3 in 24.673 as 3/1000). Students read, write, and convert decimals to thousandths into word form and fraction form (e.g., 0.563 = 563/1000 and "five hundred sixty-three thousandths").
Lesson 5
Comparing Decimals
Students place decimal digits in a laminated place value chart and compare numbers like 0.152, 0.267, and 0.289 by examining tenths, hundredths, and thousandths places. In Activity 2 students write > or < to make statements true for thousandths examples (e.g., 0.364 ? 0.318, 1.358 ? 1.360, 2.646 ? 2.645) and order groups of numbers that include thousandths. The Getting Started activity and parent notes have students use decimal grids to show equivalence (0.4 and 0.40) and the materials instruct students to look at the highest place then the next place when comparing digits.
Lesson 6
Rounding to Thousandths
Students practice place-value understanding to thousandths by writing 3.485 in word, fraction, and expanded (fractional and decimal) forms, showing tenths, hundredths, and thousandths. Students evaluate comparison statements in Unit 1 Quiz 2 Part 2 (for example: 1.320 = 1.32, 12.155 > 12.105, 0.568 < 0.658), which uses the symbols >, =, and <. The answer key identifies which comparison statements are true, indicating students check numeric equality and order for decimals with thousandths.
Lesson 10
Problem Solving
The Parent Plan Skills list explicitly states that students will "Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons." The One-Mile Run activity asks students to order race times that include hundredths and thousandths (e.g., 7.06, 7.802, 7.82), requiring students to compare decimals to place them from fastest to slowest. The Mystery Numbers activity asks students to determine numbers such as 2,971.236, which requires understanding and using digits in the thousandths, tenths, and other decimal places.
Lesson 11
Unit Test
The lesson's Skills list explicitly includes: "Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons." Student activities give explicit comparison items with thousandths (for example, 0.128 vs 0.182 and 3.045 vs 3.450) and ordering-decimal tasks (write groups of decimals least to greatest). Place-value and expanded-notation tasks (e.g., breaking 3.609 into (3 × 1) + (6 × 1/10) + (0 × 1/100) + (9 × 1/1000)) and the use of a laminated decimal place value chart provide concrete practice connecting digit meanings to comparisons.
Final Project
Number Trading Cards
Students are asked to put their cards in order from the smallest number to the greatest number, an activity that requires comparing numbers (including any decimals they collected). Students are required to collect four numbers with decimals and to show numbers in decimal expanded form, giving practice in reading and writing decimal digits. The Skills section explicitly states that students will compare two decimals to thousandths and use >, =, and < symbols, indicating an intended focus on decimal comparison.
Unit 2: Four Operations
Lesson 5
Subtracting Decimals
Students are instructed to "always write the larger number on top" when creating subtraction problems, so they must determine which of two decimals is larger. Activities require students to align decimal points and add zeros to match place values, and several practice problems and word problems use decimal numbers so students work with comparing magnitudes implicitly when choosing which number to subtract from which.
Lesson 7
Multiplying Decimals
Students represent decimals with base-10 blocks and grids (e.g., drawing tenths and hundredths) and use those models to find products such as 0.9, 1.44, 0.81, 0.045, 0.036, and 0.279. Students practice counting how many digits are to the right of the decimal in each factor and placing the decimal in the product, explicitly attending to hundredths and thousandths. Students complete problems and practice sheets that produce and require interpreting values to the thousandths place (e.g., 0.045, 0.036, 0.279).
Lesson 12
Working With PEMDAS
Students are asked to "Place the following in order from least to greatest: 0.43, 0.413, 0.314, 0.341, 0.431" on the Basic Skills Review #6, and an ordered answer is provided. The Basic Skills Review also includes decimal computation problems (e.g., product of 16.8 and 1.7 and dividing 5.4 by 5 with an expansion to 5.40) that require students to work with decimal values and positions.
Unit 3: Measurement
Lesson 1
Reviewing Customary and Metric Units
Students place decimal numbers in order in Basic Skills Review #7 problem 6, ordering values such as 2.12, 2.16, 2.09, 2.21, 2.22, 2.1, and 2.11. Students work with decimal arithmetic in problems involving multiplication and division of decimals (e.g., 266.3 × 3.9; 36.6 ÷ 0.3). Students also round 22.159 to the hundredths place, which requires attention to the thousandths digit when performing the rounding.
Lesson 2
Converting Units of Measurement
Students work with decimals when moving decimal points for metric conversions (examples show 4.5 × 10 = 45 and 4.5 ÷ 10 = 0.45 and converting 35 meters = 0.035 kilometers). Students compute with decimals in Basic Skills Review problems (4.17 × 3.9 = 16.263; 24 ÷ 2.5 = 9.6; 48.6 ÷ 0.4 = 121.5). Matching Metric Measures and other activities include decimal quantities (e.g., 2.5 liters = 2,500 milliliters) and 'Which is more?' questions that require comparing amounts expressed in different units, sometimes involving decimals.
Lesson 6
Unit Test
Students practice moving decimals and converting between metric units (kilo ... milli) and are asked to think about changing units by multiplying/dividing by ten or by moving the decimal point. Several problems present and require comparing measurements using >, <, or = (for example, comparing kilograms and milligrams, milliliters to liters, and other unit pairs). The materials include decimal values in problems (0.25 km, 1.55 km, 2.2 kg, 0.45 kg) and an explicit conversion chart that shows 0.001 for milli, which exposes students to thousandth-place values.
Unit 9: Skills Review
Lesson 2
Decimal Operations
Students generate decimal numbers to the thousandths place and answer questions identifying the digit in the tenths, hundredths, thousandths, and ones places. Students are asked to explain which of the created decimal numbers is greater. Students place given groups of decimals that include thousandths (e.g., 1.774, 2.774, 2.770, 2.604 and 0.806, 0.860, 0.086, 0.068) in ascending order, and the answer key provides sorted results.
