Multi-Digit Multiplication — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
When Grade 5 students multiply by 10, every digit shift one place to the left.
Corrected: When Grade 5 students multiply by 10, every digit shifts one place to the left.
The phrase every digit is singular, so the verb must be shifts. Multiplying by 10 moves each digit up one place value, making the magnitude ten times larger.
2. Fix the sentence:
Multiplying by 100 in Grade 5 add two zeros to a whole number.
Corrected: Multiplying by 100 in Grade 5 adds two zeros to a whole number.
Multiplying is a singular gerund subject, so the verb is adds. Times 100 moves each digit two places left, which appears as two trailing zeros for whole numbers.
3. Fix the sentence:
For Grade 5 work, 47 times 1000 equal 47,000 because three places shift.
Corrected: For Grade 5 work, 47 times 1000 equals 47,000 because three places shift.
The product expression takes a singular verb equals. Multiplying by 1000 increases magnitude by a factor of one thousand, shifting each digit three places left.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In Grade 5, 56 times 10 equals 560.
Multiplying by 10 moves the 5 and 6 each one place to the left, putting a zero in the ones place, so 56 becomes 560 with magnitude ten times greater.
2. For Grade 5 patterns, 89 times 100 equals 8900.
Times 100 shifts each digit two place values higher, so 89 grows to 8900. The two new zeros mark the empty tens and ones places after the shift.
3. Grade 5 magnitude check: 7 times 1000 equals 7000.
Multiplying 7 by 1000 moves the 7 from the ones place to the thousands place, three places to the left, leaving zeros in the hundreds, tens, and ones.
4. In Grade 5, 320 times 10 equals 3200 because each digit slides one place left.
320 already ends in zero, but times 10 still shifts every digit one place left, producing 3200 with the new zero filling the ones place.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why multiplying a whole number by 1000 is the same as shifting each digit three places to the left in Grade 5 place-value terms.
Sample answer: Each place value is ten times the place to its right. Multiplying by 10 shifts once, by 100 shifts twice, and by 1000 shifts three times. So 1000 makes the magnitude one thousand times greater, which I show as a three-place left shift.
Place values build by factors of ten, so multiplying by 1000, which is ten cubed, shifts every digit three places left, increasing the number's magnitude by a factor of one thousand.
2. How can Grade 5 students use the zero pattern to quickly compute 64 times 100 without writing the standard algorithm?
Sample answer: I think of times 100 as two place-value shifts. Sixty-four moves up two places, so 6 lands in the thousands and 4 in the hundreds. I write zeros in the tens and ones, getting 6400 without any column work.
Recognizing the times 100 zero pattern lets Grade 5 students bypass the algorithm by shifting digits two places left and filling trailing zeros, producing 6400 quickly and accurately.