Build your students’ reasoning about decimal relationships with this set of task cards and printables that focus on adding and subtracting with decimals. With this “print-and-go” resource, you’ll have everything you need to develop, strengthen, and assess your students’ understanding of estimating when adding and subtracting decimals.
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 worked on adding and subtracting with decimals. Rather than simply training my students to “line up the decimals”, I wanted them to know that when adding and subtracting decimals, the size of the sum or difference and the placement of the decimal point can be determined in advance of computing using reasoning. If you have an estimate, you can evaluate the sum or difference you get to determine whether it is reasonable and judge if your answer is likely accurate or not. Adding or subtracting places that don’t match up or incorrectly placing a decimal point will generally cause the sum or difference to be unreasonably large or unreasonably small, and so evaluating decimal sums and differences can be easy and helpful if the students have a good sense of number.
About the Cards
I wanted to develop in my students the automatic habit of estimating sums and differences, and this has always proved difficult. My students tended to focus on simply “getting the answer” and moving on to the next problem, not taking the time to think in advance of what their answer should be near or evaluating the answer they arrived at to determine if it was a reasonable size. I needed a novel way for the students to think about decimal addition and subtraction, and so I hit on the idea for these cards. Each card presents the students with an addition or subtraction expression, as well as all of the digits in the sum or difference. Rather than having to add or subtract the numbers, the students simply have to use reasoning to determine the size of the answer, and then identify where the decimal place should go in order to create a number of that size.
All of the cards are designed the same way, and so once students have an understanding of how one card works, they can 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
When working with problems like the ones on these cards, the primary strategy my students used involved estimation and relating whole number addends, minuends, and subtrahends to the given decimals. For instance, if my students had to find the difference of 13.6 and 2.89, they knew that the answer had to be around 10 since 13 – 3 = 10. When presented with the digits 1 0 7 9, they were able to reason that the decimal point went between the 0 and the 7 to create a product just above 10. If placed between the 1 and the 0, the difference would be too small, and if placed to the right of the 7, the product would be way 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. The cards can serve 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. You can even use them for a game of Scoot – the quick mental math required to solve each card lends this set perfectly to Scoot!
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 estimating sums and differences when adding and subtracting with decimals. 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 reasoning about adding and subtracting decimals.
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 adding and subtracting decimals. I designed the activities in pairs, and each pair of worksheets is 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