Help your students practice adding tenths and hundredths in fraction form, the perfect print-and-go resource for beginning fraction/decimal concepts. The 32 task cards and graphic reference sheets use hundredths grids to help students see how a fraction can be decomposed into different sets of tenths and hundredths. Extend your students’ practice (or assess their level of mastery) with the four included assessment activities. With these resources, your students will grow stronger in their understanding of key decimal concepts and lay the foundation for the work they will do with unlike denominators in fifth grade.
Save $$$ by purchasing this product as part of my Decimals on the Grid
bundle, which includes four sets of task cards, a game, a set of I Have...Who Has? cards, and more!
Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fraction (NF)
Understand decimal notation for fractions, and compare decimal fractions.
• Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (4.NF.5)
• 1 graphic reference sheet (grayscale, color, and blank)
• 1 hundredths grid resource sheet
• 32 task cards
• 8 self-checking “answer cards”
• task card answer sheet and key
• 4 assessment activities and key/rubric
About the Cards
This set is a follow-up to my On the Grid (Set A) task card and printables set. That set also addressed decimal concepts, but focused on simply identifying fraction/decimal names for the shaded portion of a tenths or hundredths grid. If you are looking for some materials to use as an introduction to decimals, On the Grid (Set A) may be a useful starting point.
Each of the cards presents students with a “decimal square” – a large square grid divided into hundredths – with a portion of the grid shaded. The students need to then choose among four addition equations that use fractions as the addends as a decimal as the sum, identifying all of the equations that match the shaded portion of the grid. For this particular set of cards, there may be more than one equation on a given card that matches the gird. Some cards have just one correct answer, but others have two, three, or even four correct answers. The question itself indicates that there may be more than one answer, but if your students have not worked with multiple choice questions for which there may be more than one correct answer, they may need some explicit assistance with this before working on these cards.
These cards use a visual model of a decimal and the concept of decomposing to help get at the idea of adding fractions with denominators of tenths and hundredths. Students examine a grid and are presented with a series of addition equations that may or may not describe the grid, most of which use mixed denominators. If students understand that one row of hundredths equals one tenth (a concept illustrated by the included reference sheet), then they can use the grid to “see” the tenths and hundredths identified in the equations. These cards will help your students build their proficiency with equivalency of tenths and hundredths (such as 4/10 = 4/100 and 70/100 = 7/10 ), making it more likely that they will be able to solve problems such as 4/10 + 19/100 when they do not have a grid.
Practicing the Concept
There are lots of ways in which you can implement the task 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.
When your students work on these cards, you may opt to have some or all of your students use base ten blocks to build each of the decimals represented by the shaded portion of the gird, using a flat for a whole, rods for tenths and units for hundredths. Have your students lay out a flat to be a constant representation of a whole, and then use the rods and units to build the shaded portion of the grid on the card. This use of a concrete representation, when paired with the visual model and numeric representations on the cards, can really help students build a strong foundation in decimal relationships as well as give them a better understanding of how a fraction or decimal can be decomposed. If a card presents the the fraction 53/100 and your students build that number with 5 rods and 3 units, they can physically regroup or separate those blocks, allowing them to better identify which equations match the given number. In addition, their understanding of fractions and decimals will be that much stronger, laying the foundation for the more complex work with decimals they will do in fifth grade.
As your students work through the cards, prompt them to consider how the decimal notation for the number represented on the grid relates to the grid itself. For instance, if 0.35 of the grid is shaded in, ask them, “Where is the 3 represented in this grid? Where is the 5?” Questions such as these can help students make sense of the numeric representation of the visual model and reinforce the value of the digits in the decimal. If you students are having trouble with such questions, break out the base ten blocks. Having your students build the decimal with base ten blocks, using 3 rods and 5 units for instance for 0.35, can help make clear that the 3 in 0.35 has a value of three tenths, represented by the 3 rods and the 3 columns of hundredths in the drawing.
One of the provided resource sheets is a set of hundredths grids, nine grids that are divided intro hundredths. You can have your students use these grids as they work with the cards rather than having them use base ten manipulatives. As they read the equations on the cards, they can shade the grids to match the equations and then check whether their shaded portion matches the one on the card. If you use Decimal Squares® materials, which use red for tenths and green for hundredths, you may have them shade in the grids in the same way, using red for tenths and green for the hundredths. For instance, if a card’s expression reads 3/10 + 42/100 , they can shade in three tenths in red and forty-two hundredths in green. Using color coding in this manner can help your students more easily make connections to the other work they have done with decimals.
Included in this set are eight “answer cards” that can serve as a resource if you use a self-paced structure for implementing the task cards. Often, I would have kids work in pairs on cards while I circulated to spot check and give feedback to pairs of students. Naturally, I would get backed up and not be able to reach as many kids until after they had already made many mistakes. I designed these answer cards so that the students could check themselves: catching errors, figuring out for themselves what they did wrong, and (hopefully) avoiding the same mistake on later cards.
Reinforcing the Concept
Also included among the printables is a full-page reference sheet that uses decimal grids to illustrate the relationship between tenths and hundredths and how a decimal can decomposed in a variety of ways into tenths and hundredths. 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 this journal inserts as guides while they work on the cards, as well as when they complete other tasks that relate to decimal concepts.
There are three versions of the reference sheet, one in grayscale, one in color, and a third with blanks grids that you can have your students color code themselves. The grayscale version presents all of the grids shaded in gray, with dotted lines used to indicate the separation between tenths and hundredths in decomposed grids. The color version uses the colors red and grid, the same ones used in Decimal Squares® materials, to emphasize the distinction between tenths and hundredths. The third version is designed to be used as an interactive, instructional resource. If you use this resource, you can give your student red and green colored pencils or markers and work together to shade in the outlined sections of the grids to show how the section can be decomposed into tenths and hundredths. Using this grid can help your students build an understanding of decomposition by involving them in making meaning of the concept at hand.
Assessing Student Understanding
The four provided assessment activities can be used to evaluate student understanding of adding tenths and hundredths in fractional form. The work the students are asked to do on the first pair of activities is similar to the questions presented on the task cards, making these activities are the perfect complement to the cards. The second pair of assessment activities ask students to shade in grids to match given expressions, create original expressions equivalent to the ones provided, and then communicate their thinking in writing. Each pair activities are formatted similarly but use different grids and numbers. I designed them this way so they could be easily used as pre/post assessments. However, you could use these activities in any way that suits your classroom routine or meets your students’ needs - homework, center assignments, paired practice, the list goes on. Answer keys and rubrics are provided for all four activities.
Please check out the preview to see all of the materials up close!
For more practice with decimal and fraction concepts, please check out the other related resources I have available –
Dog-Gone Decimals - rounding decimals task cards & printables (set a)
Dog-Gone Decimals – decimal estimation task cards & printables (set b)
Decomposing Fractions - activity card & printables bundle
Flipping for Fractions activity card set
I hope your students enjoy these resources and are able to build their proficiency with fractions & decimals. – Dennis McDonald