Place Value
Powers of Ten
Reading/Writing Decimals
Comparing Decimals
Word Problems
100
100 — Identify the value of the digit 7 in 47,312.
What is ten-thousands?
100
Multiply 23 by 10. What is the product? Explain briefly the pattern of zeros.
230. When you multiply by 10 you add one zero or shift digits left one place
100
Write the decimal for “seven and three tenths.”
7.3
100
Which is greater: 0.7 or 0.65? Explain briefly
0.7 is greater than 0.65 because 0.7 = 0.70 which has a larger tenths digit (7 > 6).
100
In Greenville, Maya is helping set up booths for Market Day in the town square. She reads that the craft tent has 
boxes of paper flowers, and each box holds 
smaller packs, with 
flowers in each pack. How many flowers are in all the boxes? Explain how the digits in 
show the pattern of multiplying by powers of 
.
flowersBrief explanation: Multiply 
. Each time you multiply by 
, every digit shifts one place to the left, so 
becomes 
, then 
, then 
.
200
200 — In the number 3.405, explain how the digit 4 relates to the digit to its right and the digit to its left (use “10 times” or “one-tenth” language).
In 3.405, 4 is in the tenths place; it is 10 times the digit to its right (the hundredths digit 0.04? — student should state 4 tenths is 10 times 4 hundredths) and one-tenth the digit to its left (the ones place 3 would be 30?
200
What is 4.7 × 10? What happens to the decimal point?
47. The decimal point moves one place to the right when multiplying by 10.
200
Write 0.406 in words (include the place of the last digit).
Four hundred six thousandths
200
Order these from least to greatest: 0.4, 0.39, 0.401.
Least to greatest: 0.39, 0.4, 0.401.
200
Later, Maya visits the Greenville Seed Shop to label jars of sunflower seeds. One jar holds 
ounces of seeds, and another larger jar holds 
ounces. How many times as much seed does the larger jar hold as the smaller jar? Use the pattern in the number to show how multiplying by 
changes the value of a digit.
Later, Maya visits the Greenville Seed Shop to label jars of sunflower seeds. One jar holds 
ounces of seeds, and another larger jar holds 
ounces. How many times as much seed does the larger jar hold as the smaller jar? Use the pattern in the number to show how multiplying by 
changes the value of a digit.
Answer: 
times as much
Answer: 
times as much
Brief explanation: Since 
, the larger jar holds 
times as much seed. Multiplying by 
moves each digit one place to the left, so the 
moves from ones to tens and the 
moves from tenths to ones.
Brief explanation: Since 
, the larger jar holds 
times as much seed. Multiplying by 
moves each digit one place to the left, so the 
moves from ones to tens and the 
moves from tenths to ones.
300
Write a number in standard form when given: 6 ten-thousands, 2 thousands, 9 tens, and 5 ones.
What is 62,095?
300
Multiply 0.356 by 100. Show the result and explain how you moved the decimal point.
35.6. Multiply by 100 moves the decimal two places to the right.
300
Convert 12.5 into a decimal and explain what the 5 represents.
12.5; the 5 is in the tenths place so it represents five tenths or 0.5.
300
Compare using <, >, or = : 3.405 ___ 3.45. Explain how you determined the relation.
3.405 < 3.45 because at the hundredths place 0 < 4 after matching whole-number and tenths digits.
300
At the Greenville Train Station, Maya sees three signs showing the weights of travel bags: 
pounds, 
pounds, and 
pounds. Write these decimals in order from least to greatest. Then explain how the value of each digit helps you compare the numbers.
Answer: 
Brief explanation: Compare place values from left to right. All have 
ones. Next, compare tenths: 
has 
tenths, so it is the smallest. Between 
and 
, the tenths are both 
, so compare hundredths: 
, so 
is less than 
.
400
A digit is underlined: 8,3̲4̲5̲,9̲2̲ (read left to right: 8 3 4 5 9 2 with digits 4 and 9 underlined). For each underlined digit, state its place value and compare the two underlined digits (which is 10 times the other?).
If 4 is in the hundreds place its value = 400; if 9 is in the tens place its value = 90. The digit in the hundreds place is 10 times the digit in the tens place.
400
Write 9 × 10^3 as a whole number and explain how the exponent tells you what to do.
The exponent 3 tells you to multiply by 10 three times (or move the decimal/ digits three places
400
Write these numbers in decimal form and in words: (a) twelve thousandths, (b) three and five hundredths.
(a) 0.012 — “twelve thousandths.” (b) 3.05 — “three and five hundredths.”
400
Two students compare 0.507 and 0.57. One says 0.507 is greater because 507 > 57. Explain the error and give the correct comparison.
Error: comparing digits without aligning place value. Correct: 0.507 < 0.57 because 0.507 = 0.507 and 0.57 = 0.570; at the hundredths place 0 < 7.
400
That afternoon, Maya buys ribbon at Greenville Crafts. The clerk measures three pieces: 
yards, 
yards, and 
yards. Write the ribbon lengths in order from greatest to least. Use 
, 
, or 
to compare the decimals and show how the place value of each digit helps.
Answer: 
Brief explanation: Write 
as 
to compare easily. Then compare: 
. The tenths, hundredths, and thousandths places show which number is greater.
500
Explain why the digit 5 in 50,000 is 10 times the value of the digit 5 in 5,000 and one-tenth the value of the digit 5 in 500,000. Give a one-sentence explanation using place-value language
Example answer: The 5 in 50,000 represents 50,000 which is 10 times 5,000 (the 5 in 5,000) and one-tenth of 500,000 (the 5 in 500,000); moving one place left multiplies value by 10.
500
A decimal 12.034 is multiplied by 1,000. Show the product and explain the rule for multiplying a decimal by powers of ten, using the exponent notation.
12,034. Multiplying by 1,000 moves the decimal three places to the right
500
A student wrote “five hundred twenty-three and forty-six thousandths” as 523.046. Is this correct? Explain why or why not and give the correct decimal if needed.
Yes. 523.046 is correct for “five hundred twenty-three and forty-six thousandths
500
Provide a strategy (in 2–3 sentences) to compare 0.399 and 0.4, then state which is larger and why using place value language
Strategy: Line up the decimals or add zeros to make place values clear (0.399 vs 0.400). 0.400 is larger because 0.399 is three hundred ninety-nine thousandths while 0.400 is four hundred thousandths
500
At the end of the day, Greenville’s parade organizer records the distances of three practice routes: 
miles, 
miles, and 
miles. Maya needs to round each distance to the nearest hundredth for the parade map. What is each rounded distance, and which route is the longest after rounding?
Answer:
The longest route after rounding is 
miles.
Brief explanation: To round to the nearest hundredth, look at the thousandths digit. In 
, the thousandths digit is 
, so the hundredths digit stays 
. In 
, the thousandths digit is 
, so the hundredths digit 
rounds up to 
. In 
, write it as 
, so it rounds to 
.