Build your students’ reasoning about decimal relationships with this set of task cards and printables that focus on multiplying with decimals and whole numbers. With this “print-and-go” resource, you’ll have everything you need to develop, strengthen, and assess your students’ understanding of the relationship between factors and products when multiplying with decimals and whole numbers.
Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fractions (NF)
Perform operations with multi-digit whole numbers and with decimals to hundredths.
• Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (5.NBT.7)
• reference sheet
• 32 task cards
• task card answer sheet and key
• 8 self-checking “answer cards”
• 4 assessment activities
• rubric and answer key for assessment activities
I designed this set of cards to build my students’ reasoning skills when we began working on multiplying with decimals. I didn’t want to simply teach them a rule that they would write in their journals and then rotely follow. My goal was for them to think about the size of the factors they were multiplying and understand that the placement of the decimal didn’t just follow a rule – it also made numeric sense! My students noticed that the number of decimal places in the factors equaled the number of decimal places in the product in most cases, but they also saw that there were some multiplication equations that did not follow this pattern (e.g., 4.5 x 6 = 27). I wanted my students to know that while a rule can be used in most situations to determine the placement of the decimal point in a product, reasoning
can also be used. An incorrectly-placed decimal point will always cause the product to be unreasonably large or unreasonably small, but a correctly-placed decimal will make the size of the product be just right.
About the Cards
Each card presents students with a pair of factors as well as the digits, but not the decimal point, in the product of those factors. The students simply have to identify the correct place in which the decimal point belongs.
The factors on the cards are a mix of whole numbers and decimals. The largest place in any of the factors is the hundreds place, and the smallest place in any of the factors is the hundredths place. In the products, the smallest place used is the thousandths place, and most products do not extend lower than the hundredths place.
All of the cards are formatted in the same way, and so once students have an understanding of how one card works, they can easily complete all of the cards. Since the format of these cards is different than ones I had done before, I presented one as a sample and had the entire class work through the card together. After we had done this sample, the students understood how to use the cards, and were able to complete the rest with little to no assistance.
Please check out the preview to see all of the materials up close!
Using the Cards
Before using these task cards, I had my class practice using reasoning to determine the placement of the decimal point in the product of whole number and decimal factors. By the time they used these cards, they were able to use estimation to figure out where the decimal should be placed. Some of the students were able to do all of the work mentally, while some needed to write down some of their thinking (such as writing 30 x 7 = 210 when examining the factors 31.8 x 7.15). Very few of my students relied on counting decimal places, using estimation instead, and since I chose factors for some of the cards so that the number of decimal places in the factors did not match the number of decimal places in the product, students were forced to use a strategy other than simply counting decimal places.
The primary strategy my students used involved estimation and relating whole number factors and products to the given decimals. For instance, if my students had to find the product of 3.6 and 9.5, they knew that the answer had to be larger than 27 since 3 x 9 is 27. When presented with the digits 3 4 2, they were able to reasons that the decimal point went between the 4 and the 2 to create a product in the 30s. If placed between the 3 and the 4, the product would be too small, and if placed to the right of the 2, the product would be too large.
There are lots of ways in which you can utilize these cards. You can have the students work on them independently, working through the task cards on their own. The students can work on them in pairs or small groups, completing all the task cards in one session. You can use them in centers, having the students complete 6-8 task cards a day over the course of the week. You can even use them as a variation of “problem of the day”, giving each student 1 sheet of 4 cards to glue in their journals and solve, one sheet per day for eight days.
Reinforcing the Concept
One of the printables includes a reference sheet that I designed for my students to glue in their math notebooks. The graphic reference sheet illustrates two strategies for using reasoning to determine the placement of the decimal point in the product of whole number and decimal factors. When I use reference sheets of this size, I have the students fold the sheet from the bottom to the top, not quite halfway, creasing the paper so that the title of the sheet is visible. When the students glue the folded sheet in their journals, the title is then visible so that students can more easily find it when they need to refer to the information on the sheet. Your students can use the journal insert as a guide while they work on the cards, as well as when they complete other tasks that relate to multiplying multi-digit numbers using the area model.
Assessing Student Understanding
The four provided assessment activities can be used to evaluate student understanding of how to use reasoning to determine the placement of the decimal when multiplying decimals and whole numbers. I designed the activities in pairs, and the activities in each pair are formatted similarly, and have similar types of questions, though the numbers on each are different. 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 practice with decimal concepts, please check out the other related resources I have available –
Bird Brains - x and ÷ with powers of ten task cards and printables (set a)
Dog-Gone Decimals - rounding decimals task cards & printables (set a)
Dog-Gone Decimals – decimal estimation task cards & printables (set b)
Placing the Value - task cards + printables set
Grid Match-Up - relating tenths and hundredths game, activity cards, printables
On the Grid - modeling decimals and fractions task cards & printables (set a)
On the Grid - adding tenths and hundredths task cards & printables (set b)
I hope your students enjoy these resources and are able to build their proficiency with decimals. – Dennis McDonald