Help your students become experts with tenths and hundredths, developing their understanding of how these fractions relate with this set of games, activity cards, reference sheets, and assessment activities.
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)
• 2 graphic reference sheet
• 2 blank tenths & hundredths grids templates
• 2 gameboards & 4 pairs of spinners
• 2 recording sheets
• 1 set of 32 “I Have…Who Has?” – provided as a full set and 16-card “half-sets”
• master list of question and answers
• 4 assessment activities and key/rubric
About the Resources
Fluency with equivalent fractions is a major milestone in Common Core Math in the intermediate grades, grade 3 through 5. Students begin working with fraction equivalence starting in third grade, and the work they do in third and fourth grades builds the foundation they need for renaming fractions to add and subtract unlike denominators in fifth grade.
While students in fourth grade do not need to be able to add and subtract unlike denominators using a formal procedure, the decimal standard 4.NF.5 provides a “baby step” towards this by requiring students to be able to add tenths and hundredths to create a sum with a denominator of 100. The games, activity cards, and resources in this set were designed to help develop students’ understanding of the relationship between tenths and hundredths, increasing their fluency with identifying pairs of equivalent fractions that use 10 and 100 as denominators and building on that fluency to help them practice decomposing decimal fractions into tenths and hundredths.
The Grid Match-Up game is simple and requires only some colored tokens and a plastic spinner (or a pencil and a paper clip for a makeshift spinner). There are two gameboards – Gameboard A, which features images of shaded hundredths grids (e.g., 0.40 and 0.80) ,and Gameboard B which features shaded tenths grids. Each gameboard has two pair of spinners, with the first pair featuring tenths or hundredths in fraction form and the other pair featuring numbers in decimal form. The boards and the spinners are paired so that they use different denominators. For example, while Gameboard A features hundredths grids, Spinners A1 & A2 and A3 & A4 feature tenths. By pairing boards and spinners that use different denominators, students need to recognize the number of tenths that are equivalent to a given number of hundredths, and vice versa. With two different gameboards and four pairs of spinners, your students can play this game again and again and have a different experience each time. The more your students match tenths and hundredths that are equivalent, the more automatic they will become in recognizing that 2/10 equals 20/100 and 70/100 equals 7/10 .
As your students play, you can have them use one of the two included recording sheets to practice writing equations with tenths and hundredths. One recording sheet has spaces for two fractions (with labels to reinforce the meaning of the terms numerator and denominator), while the other recording sheet has spaces for a decimal and a fraction.
Reinforcing the Concept of Equivalency
Beyond the game, this set includes other resources to help your students see the relationship between equivalent tenths and hundredths. There is a full-page reference sheet that presents students with ten pairs of shaded grids, from 1/10 and 10/100 to 10/10 and 100/100 . 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. You can have your students use this reference sheet while they play the game, as well as when they complete other tasks that relate to decimal fractions. You can even use the reference sheet as the springboard for a classroom discussion and/or a journal writing activity, asking your students to identify any patterns evident in the numerators and denominators in the equivalent fraction pairs and supporting their claims with evidence from the reference sheet.
If you want your students to build their own understanding of equivalence with decimal fractions, use the tenths and hundredths grid templates. This resource presents blank tenths and hundredths grids in pairs so students can do their own shading. Have them shade in one tenth in one grid and then ten hundredths in the next grid, writing an equation beneath the two grids to show that 1/10 = 10/100 . If you use the Decimal Squares® with your students, you might have them use colored pencils when shading, coloring tenths in red and hundredths in green to match the colors used on the Decimal Squares® grids. By having students create their own grids, rather than simply examining pre-made grids, they will have to make meaning of the relationship between tenths and hundredths and are more likely to internalize that relationship.
Composing and Decomposing
Once your students have a firm grasp on the relationship between tenths and hundredths, build on that foundation to have them practice expressing decimal fractions as the sum of a certain number of tenths and hundredths. If they are able to identify that 3/10 = 30/100 , it’s just a small hop to recognizing that that 37/100 = 3/10 + 7/100 . Decomposition is a major concept in Common Core, with students being asked to decompose whole numbers, shapes, fractions, even angles. While the standard 4.NF.5 does not specifically mention decomposing, I felt that my students’ previous work with decomposition of fractions made this an excellent way to introduce the concept of combining tenths and hundredths.
The second full-page reference sheet uses tenths and hundredths grids to show how a given decimal fraction can be represented as a set of tenths and some extra hundredths. Two complete examples are presented for students, and then students are give two grids and asked to decompose the given fraction into tenths and hundredths. Have your students continue their practice by using the Break It Up! resource sheet to create their own models of fraction equations. Students are presented with a hundreds grid followed by a tenths grid and another hundreds grid. You can have students shade in a certain number of hundredths (such as 53/100 ) in the starting grid, and then shade in the number of tenths ( 5/10 ) and hundredths ( 3/100 ) that the original fraction can be decomposed into, recording an equation to match the model they created. Then have them try it in reverse, selecting a certain number of tenths and a certain number of hundredths, and then using the grids to show their combined sum.
Once your students have explored with combining tenths and hundredths and decomposing fractions into separate tenths and hundredths, use the “I Have…Who Has?” card set to help reinforce those concepts. Each card presents a shaded hundredths grid. Students identify the fraction of the grid shaded, such as 82/100 , and then read an expression that uses tenths and hundredths, such as 3/10 + 8/100 . The student with the next card identifies the fraction (38/100 ) and then reads the next expression.
There is a full set of 32 “I Have…Who Has?” cards, two smaller, 16-card “half-sets” that use the same questions and answers as the full 32-card sets, and a master list of the questions and answer on the cards. The cards in the set have a unique question and answer, and none of the questions or answers are repeated. There is no specific starting card as the 32 cards loop around. Any student can begin, and since none of the questions or answers are repeated, the cycle will eventually lead back to whatever student began the activity.
Included with the cards is a master list all the questions and answers on each of the cards. If you want to follow along with the students, you can have the student with a particular card begin, and use the master list to keep track of what card will be up next in case a student needs a hint. Alternately, you can have any child begin, and if you locate their statement and question on the sheet, you will be able to use the list to follow along in sequence.
This set is versatile, designed to accommodate both large and small groups. There are 32 cards in the full-set to accommodate large classes. You can still use the entire set even if you don’t have 32 students by having some students hold two cards at once. However, if you have much fewer than 32 students and you want to get more use out of each set, I have included a pair of “half-sets” for each set of 32 cards. These half-sets contain 16 cards and are identified as Set A1 and Set A2. They have the exact same numbers and expressions from the original sets of 32, but they are split into two groups and have their “ending” cards altered so that the 16th card loops back to the 1st card and the 32nd card loops back to the 17th card. If you have a class size closer to 16, you can use a half-set, such as Set A1, doubling up cards or kids as needed if you don’t have exactly 16 kids, and use the half-set with your class one day, saving the other half-set for a different day.
After your students have had practice with equivalent tenths and hundredths, you can use the first pair of assessment activities to check your students’ understanding. These one-page activities ask students to show their understanding of decimal fraction equivalence in a number of ways: shading a decimal grid, creating equations with fractions and decimals, and writing about the patterns evident in pairs of equivalent fractions. The two activities are formatted similarly but use different numbers, making them ideal for pre/post assessing. 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.
After your students have had practice with combining and decomposing tenths and hundredths, you can use the second pair of assessment activities to check your students’ understanding. These one-page activities ask students to show their understanding of decimal relationships by creating grids to match given expressions and then comparing two fractional amounts that are presented as separate tenths and hundredths. Like the first pair of assessment activities, this pair requires students to respond to a given question in writing, allowing you to see how clearly and completely they can communicate their mathematical thinking. These two activities are also formatted similarly but use different numbers, allowing you to use one as a pre-assessment and one as a post-assessment. 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.
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For more practice with decimal and fraction concepts, please check out the other related resources I have available –
On the Grid - modeling decimals and fractions task cards & printables (set a)
On the Grid - adding tenths and hundredths task cards & printables (set b)
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 and decimals. – Dennis McDonald