Students identify digits in specific places (e.g., tens, hundreds, thousands) and compute related sums and differences (questions: "What digit is in the tens place?"; "What number is 10 more than this number?" ). Students write numbers in expanded form and expanded notation that show each digit multiplied by its place value (examples such as (3 x 1,000,000) + (4 x 100,000) ... and expanded notation answer keys). The parent prompts ask students to state the value of a digit in context (e.g., "What is the value of the digit 4 in this number? (400)").

Students encounter the exact language of the standard in the "Things to Know" section: "A digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left." Students complete guided practice on the Digit Values and Values Left and Right pages that have multiple worked examples and problems (e.g., 200 is 10 times 20; 54 ÷ 10 = 5.4; 1.2 ÷ 10 = 0.12). Students also practice moving the decimal point and computing multiples and one-tenths across whole numbers and decimals with fill-in-the-blank items and calculation problems.

Students compare place values using the laminated grids (showing 0.6, 0.06, 0.006) to see that digits to the right have one-tenth the value of digits to the left. The lesson asks direct questions and examples (Q4: "Each decimal place value is how much of the size of the value before it? — one tenth") and has tasks where students write the value of a digit (e.g., "What is the value of 3 in 24.673? Answer: 3/1000"). Expanded form and expanded notation examples show digits multiplied by 10, 0.1, 0.01, etc., and whole-number expanded examples (e.g., 463 -> 400 + 60 + 3 and (9×10^2)+(5×10^1)+4) connect the 10× relationship across places.

Students color 4 spaces on a tenths grid and 40 spaces on a hundredths grid to show 0.4 and 0.40, directly demonstrating that the same quantity can be represented in different places. Students place digits in a labeled place-value chart (ones, tenths, hundredths, thousandths), write numbers such as 0.152, 0.267, and 0.289, and compare them by examining digits in the tenths, hundredths, and thousandths places. Parent prompts and instructions remind students that tenths are bigger than hundredths and hundredths are bigger than thousandths, and students order and compare decimals to thousandths on worksheets and problem-solving tasks.

Students write decimals in multiple forms including decimal expanded notation and fractional expanded notation (e.g., (3 × 1) + (4 × 0.1) + (8 × 0.01) + (5 × 0.001)). Students convert expressions using place-value weights into decimal numbers (for example, (8 × 1/10) + (3 × 1/100) + (2 × 1/1000) = 0.832). The materials direct students to use place value understanding to round decimals and instruct them to look at the digit to the right of the target place when rounding.

Students multiply and divide whole numbers and decimals by powers of ten (Activity 3 matching, Basic Skills Review, and the answer keys showing 10 × 1000 = 10,000, 0.1 × 10 = 1, etc.). Students use a number line of powers of ten (10^0 to 10^6) and fill in exponential notation for large numbers (Student Activity Page and 'Beyond a Million' sheet). Parent prompts and wrap-up questions ask students to say what number is ten times more than a given number and to compute one-thousandth times 10, reinforcing multiplication/division by 10.

Students repeatedly multiply and divide numbers by 10 and powers of 10, for example completing problems like 5 × 1,000, 100 × 6, and sequences such as 34,000 ÷ 10 = 3,400 then ÷ 10 = 340, showing digits shifting positions. Students practice moving digits left when multiplying and right when dividing and use exponent notation (e.g., 5 × 10^3) to represent these operations on multiple activity pages. Students complete matching and pattern activities that tie the number of zeros or the exponent to how many places the digits or decimal point move.

The Parent Plan explicitly lists the targeted skill that a digit in one place represents 10 times the value of the place to its right and 1/10 of the place to its left. Activity 1 has students multiply and divide decimal numbers by powers of 10 and a parent prompt asks the child to explain how digits and the decimal point move when multiplying/dividing by powers of 10. Activity 3 asks students to write numbers in expanded and fractional expanded form and to compare and order decimal times, which requires decomposing digits by place value. The Wrap-Up and Things to Review sections explicitly describe moving digits/decimal points for powers of 10 and steps for rounding, reinforcing place-value shifts by factors of 10.

Students write numbers in fraction-expanded and place-value expanded notation such as (4 × 10) + (6 × 1) + (5 × 1/10) and (2 × 1) + (4 × 1/10) + (7 × 1/100), showing the value contributed by each digit. Students complete problems that multiply and divide numbers by 10 and powers of 10 (e.g., 12.35 × 10, 2.56 × 10^2, 498 ÷ 10^2 = 4.98, 2.98 × 10^3 = 2,980). Students answer place-value identification questions and tasks that ask for amounts like "What number is 10 more than this number?" and calculating values when a digit's place is shifted (e.g., multiplying 6.21 by 10^4).

Students are asked to represent numbers in expanded (place-value) form (example: 1,383 shown as 1,000 + 300 + 80 + 3) and to show numbers in at least three different forms, including decimal expanded form and powers of ten/scientific notation. Students must collect real-world multi-digit and decimal numbers (including numbers to the hundredths and numbers between thousands and millions) and record multiple ways to show each number on the Number Collection sheets. Students must order cards from smallest to greatest and compare numbers, and the Parent Plan Skills explicitly list using place-value understanding to round and comparing decimals based on the meanings of digits.

Students practice treating digits according to their place values when forming partial products (for example, 185 × 5 = 925 and 185 × 20 = 3,700; 314 × 3, 314 × 20, and 314 × 500 are computed as separate partial products). The materials instruct students to use zero placeholders and to stack partial products when using the standard algorithm for multiplication. Students are also repeatedly told to "line up the number places correctly" when adding and subtracting multi-digit numbers.

Students practice removing and adding zeros to simplify division problems (e.g., 1,600 ÷ 8 -> 16 ÷ 8, then add two zeros to the quotient). Students use base-ten blocks to build numbers (make 72 with tens and ones) and are instructed to ungroup tens into ones to redistribute when dividing into equal groups. The lesson also models simplifying multiplication/division by canceling zeros (e.g., 1,200 ÷ 30 -> 120 ÷ 3 and then adding zeros back), which has students work with place shifts by factors of ten.

Students read and answer questions that explicitly state that each decimal place is ten times smaller than the place before it, with examples (hundredths is ten times smaller than tenths; thousandths is ten times smaller than hundredths). Students match decimal numbers to base-10 block representations and are instructed to bundle blocks when possible, which has them group ten of a smaller unit into one of the next larger unit. Students use a laminated decimal place-value chart and are shown that adding zeros (3.4 = 3.40) does not change value, reinforcing equivalence across adjacent places.

Students work with tenths and hundredths in multiple examples (e.g., discussions about zeros in the hundredths place and the tenths place being required for eight hundredths). Students practice aligning decimal points and are instructed to add zeros to whole numbers (e.g., $5 as $5.00) when performing subtraction, which uses place-value notation. Students apply decimal place notation when solving money problems and deciding when trailing zeros may be dropped or must be kept.

Students draw and use base-10 blocks to represent decimals and explicitly exchange 10 units (hundredths) for 1 rod (tenth) and 10 rods (tenths) for 1 flat (one whole). Students use these drawings to compute products (e.g., showing 2 × 0.45 = 0.9 by converting 10 hundredths into 1 tenth) and are prompted to ‘make sure that he is exchanging blocks correctly.' Grids and activities (e.g., shading tenths and counting overlapping hundredths) reinforce that a tenth equals ten hundredths and that each place represents different sized units.

Students model decimals with base-10 blocks and are instructed to split each flat into 10 rods and each rod into 10 units, drawing these models to represent numbers like 2.8. The lesson directs students to use a laminated decimal place-value chart and examples (e.g., 24 = 24.0 = 24.00) and to count/move decimal places when dividing, linking shifts in place to multiplying or dividing by 10. Activities require students to place decimals correctly in long division and to explain moving the decimal in the dividend the same number of places as in the divisor, which reinforces place-value shifts.

Students complete problems that require multiplying by powers of 10, such as 43.76 × 10 (answer 437.6) on the Unit Review sheet and 48.76 × 100 (answer 4,876) on the Unit Test. Several computation and decimal problems (e.g., multiplying/dividing decimals and whole-number place shifts) provide practice that implicitly uses place-value shifts when multiplying by 10 or 100.

The lesson notes that the metric system is "based on the number 10," and students complete Basic Skills problems that involve powers of ten (e.g., "What is 37 times 10 to the power of 6?") and ordering/working with decimals (ordering decimal numbers and rounding to the hundredths). Students also work with operations that shift decimal places (e.g., division by 0.3 and other decimal calculations) which requires some facility with place-value movement.

The lesson explicitly teaches multiplying and dividing by powers of ten (e.g., "when you multiply a whole number by 10, you just add a zero") and shows decimal shifts (examples 4.5 × 10 = 45 and 4.5 ÷ 10 = 0.45). The metric "stairs" graphic states that each step is "10 times the size of the one to the right and 1/10 the size of the one to the left," and students practice counting steps to move the decimal when converting (e.g., 35 meters = 35,000 millimeters). Students complete activities that require moving the decimal left/right and using powers of ten for conversions across kilo–milli prefixes.

Students are asked to think about how metric conversions are based on powers of ten and to change units by multiplying or dividing by ten or by moving the decimal the correct number of spaces. The student pages include a flowchart (kilo, hecto, deka, BASE, deci, centi, milli) with arrows indicating conversion by factors of 10 and a mnemonic to remember the order. Exercises require students to convert between units by factors of 10, 100, and 1,000 (for example, converting kilograms to grams and grams to milligrams) and to fill in conversion boxes showing Kilo = 1000, Hecto = 100, Deka = 10, Deci = 0.1, Centi = 0.01, Milli = 0.001.

The lesson uses expanded form to break multi-digit numbers for area models (e.g., "break 64 into 60 and 4, and 72 into 70 and 2") and shows how those parts form smaller rectangles whose areas are added. The Parent Plan and activities explicitly mention using the expanded form of mixed numbers and decomposing dimensions into whole- and fractional-part tiles for multiplication. Several examples and problems require students to decompose numbers (e.g., 3 1/2 into 3 and 1/2; 5 1/4 into 5 and 1/4) and use those parts in calculations.

Students complete comparison problems that directly involve dividing by 10 and 100 (e.g., 360 ÷ 5 vs 360 ÷ 10 and 6700 ÷ 100 vs 6700 ÷ 10). The lesson prompts students to work with dividing decimals and to pay attention to decimal-point placement, and one discussion prompt suggests solving 1800 ÷ 60 by "removing the same number of zeros in both numbers." Students also match division problems where divisors include 0.2 and 18, requiring decimal-place reasoning.

Students are asked to identify digits in specific places (tenths, hundredths, thousandths, and ones) on the decimal creation page. Students convert decimals into expanded form and matching fraction and word forms on the "Representing Decimal Numbers" sheet (e.g., 1.42 = 1 + 0.4 + 0.02; 0.381 = 0.3 + 0.08 + 0.001). Students complete a "Powers of 10 and Exponents" chart that links number form, expanded form, and exponent form for powers of 10.