Help your students practice using place value relationships to multiply and divide with powers of ten with this double set of task cards and assessment activities. With 64 task cards and 8 assessment activities, as well as a place value mat and digit cards to allow your students to build and manipulative the numbers as they multiply and divide, you have everything you need in one “print-and-go” package.
Common Core State Standards for Mathematics addressed:
Numbers and Operations in Base Ten (5.NBT)
Understand the place value system.
• 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. (5.NBT.2)
• place value mat & digit cards
• 2 sets of 32 task cards (64 in all)
• 8 self-checking “answer cards”
• answer sheet and key
• four one-page assessment activities
• four half-page, "exit ticket" assessments
• scoring guide and rubric for assessment activities
This set of task cards is designed as an introduction to multiplying and dividing whole numbers and decimals by powers of ten, and the cards and accompanying resources offer multiple opportunities for differentiation. There are two sets of 32 task cards, and the questions and answers on the two sets do not overlap. Set A1 presents students with expressions that use powers of ten in standard form (e.g., “What is the quotient of 4.5 ÷ 100?”), while Set A2 uses whole number exponents to represent powers of ten (e.g., “What is the quotient of 68.92 x 10^3 ?”). The largest power of ten used in the expressions is 10,000 (10^4). Each set uses a different color border (purple for Set A1 and blue for Set A2). In addition, each card is labeled as belong to Set A1 or Set A2 to help distinguish them if you decide to print the cards in grayscale.
When introducing the concept of multiplying and dividing by powers of ten, I felt that it would be better for my students to begin with the standard form of powers of ten rather than the exponent form. While my students had done work with writing the powers of ten in exponent form, I felt that the abstractness of such a newly-introduced concept would make it more difficult for them to focus on the patterns in the factors/products and dividends/divisors/quotients. By using the standard form of powers of ten, my students didn’t have to think about what 10^3 or 10^2 represented as they worked with the equations, but simply how the placement of the digits in the factor or dividend compares to the placement of the digits in the product or quotient. Once they realized the patterns evident when multiplying and dividing by powers of ten, I then had them work with equations that used exponents to denote powers of ten.
You can use these two sets of cards in whatever way best meets your own students’ needs. You may choose to use them as I did, having the students work with Set A1 first and the follow-up with Set A2. You may also have some of your students work with Set A1 and others work with Set A2. You can even intermingle the two sets, mixing together some cards from Set A1 and some cards from Set A2. The two sets share one answer key (for example, the correct answer for Card 5 from Set A1 is “c”, and the correct answer for Card 5 from Set A2 is also “c”), allowing you to mix the two sets together and still be able to accurately grade your students’ work.
Have your students use the place value mat and digit cards as they work with the multiplication and division expressions on the cards. The mat and cards may be especially useful if you are using these cards to help develop your students’ understanding of the patterns evident when multiplying and dividing by powers of ten. You can have your students build the original number (the first factor or the dividend from the card) and then, beneath it, build the new number (the product or the quotient). As your students build each pair of numbers, they can compare the placement of the digits and how they have shifted to the right or to the left. For instance, if the student has a card with the expression 46.3 ÷ 100, they would build 46.3 on the mat, and then build the quotient, 0.463. Having the two numbers side by side can allow students to more easily see that each digit in the quotient is two places to the right of the digit’s original placement. You may choose to have all of your students use the mats or you may use the materials as a way to differentiate for those students who are having trouble identifying the pattern in how the digits shift when a number is multiplied or divided by a power of ten.
The provided assessment activities can be used to evaluate your students’ mastery of the concept of multiplying and dividing by powers of ten. The first four assessment activities are full-page in length, and they are formatted similarly and have similar types of questions, though the numbers on each are different. The first two assessment activities (activities a and b) use standard form to represent powers of ten, just as the cards in Set A1 do, and the other two assessment activities (c & d) use exponents to denote powers of ten, as on the cards in Set A2. In addition to these four assessment pages, you also have four half-page, “exit ticket”-style assessments. Two of them use standard form for the powers of ten and two use exponent form. Each of these exit tickets present students with a series of equations and ask them to write about the patterns evident in the equations. Keys and rubrics are provided for all of these assessment activities.
You can use these activity pages in a variety of ways. You could give one as a pre-test, then teach your lesson and allow students to practice with the task cards, and then give the second worksheet as an independent post-test. You could also have the students work on the task cards, then complete one of the worksheet as guided practice with yourself, a partner, or a small group, and then give the second worksheet as an independent assessment. The worksheets could also be given as homework, center assignments, or any other purpose that fits your teaching style or classroom routines.
For more resources that address concepts in the domain of number and operations in base ten, please check these out –
Super Powers of Ten - task cards + printables (set a)
Placing the Value - task cards + printables set
Self-Checking Math Riddles – Comparing Place Values: 10x Larger and 10x Smaller
I hope your students enjoy these resources and are able to build their proficiency with multiplying and dividing with powers of ten. – Dennis McDonald