This 5th grade math workshop pulls the whole Common Core place value cluster onto one worksheet. Students state that a digit one place left is worth 10 times as much, using the 4s in 44.4 and the 5s in 550, then shift decimals with powers of ten (3.45 × 10², 716 ÷ 10²). A chart swaps 4.628 and 73.059 between standard, expanded and word form, six circles get >, <, or = for pairs such as 0.608 and 0.68, and rounding closes with a lab balance reading 4.856 grams.
5.NBT.1
“Recognize that in a multi-digit number, 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.”
Question 1 compares the two 4s in 44.4 and the two 5s in 550, filling in 1/10 and 10 times.
5.NBT.2
“Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.”
Question 2 shifts decimals in both directions: 3.45 × 10² = 345 and 716 ÷ 10² = 7.16, with exponents naming the number of places.
5.NBT.3.a
“Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 x 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).”
The question 3 chart moves 4.628, 73.059 and 12.045 between standard, expanded and word form.
5.NBT.3.b
“Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.”
Question 4's six comparisons and question 5's ordering of 2.083 through 2.803 both hinge on digit-by-digit place value.
5.NBT.4
“Use place value understanding to round decimals to any place.”
Question 6 rounds three decimals to three places each, and question 7 rounds the 4.856 gram balance reading.
Students complete statements about the 4s in 44.4 and the 5s in 550, then evaluate four exponent problems: 3.45 × 10², 0.82 × 10³, 716 ÷ 10² and 58.2 ÷ 10¹.
A three-column chart converts between forms: 4.628 needs its word form, seventy-three and fifty-nine thousandths needs its standard form 73.059, and 12.045 needs the expanded form (1 × 10) + (2 × 1) + (4 × 1/100) + (5 × 1/1000).
Six pairs take >, <, or =, including the equal pair 4.350 and 4.35 and the near-miss 18.406 versus 18.460. Question 5 then orders 2.308, 2.38, 2.083 and 2.803 from least to greatest.
Students round 6.472, 15.938 and 0.706 to the nearest whole, tenth and hundredth, then round a mineral specimen's balance reading of 4.856 grams and explain why the tenths digit climbs from 8 to 9.
Unit review day
The four sections match the four skills on most place value tests. Set a ten-minute timer per section and rotate, then spend the last stretch on whichever section produced the most hands.
Diagnosing shift errors
Watch question 2c. Students who write 71,600 for 716 ÷ 10² are moving the decimal the wrong way, and the Remember callout beside question 1 is the fix to point at.
Science tie-in
Question 7's digital balance mirrors what students see in a lab. Round the 4.856 gram reading as a class, then have students defend the 8-to-9 tenths change in writing.
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