# Adding & Subtracting Unlike Denominators - task card + printables bundle

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### PRODUCT DESCRIPTION

Build your students’ proficiency with adding and subtracting fractions and mixed numbers with unlike denominators. This “print-and-go” resource has everything you will need to build, reinforce, and assess key fifth grade fraction concepts: reference sheets, task cards, self-checking puzzles, and assessment activities.

NOTE: This bundle contains four products available separately: Foxy Fractions, Ferret-y Fractions, Fishy Fractions, and Self-Checking Riddles. Purchasing this bundle saves you over 20% on the cost of the individual products. In addition, you will receive 2 bonus sets of I Have…Who Has? cards that are only available in this bundle!

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Common Core State Standards for Mathematics addressed:
Numbers and Operations – Fractions (5.NF)
Use equivalent fractions as a strategy to add and subtract fractions.
• Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) (5.NF.1)
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Included:
• 4 different graphic reference sheets
• 3 sets of 32 task cards – 96 cards in all
• 7 self-checking puzzles and keys
• 12 assessment activities and keys/scoring guides
• 2 sets of 32 I Have…Who Has? cards, provided as full sets and half-sets

Foxy Fractions

I designed these cards as a beginner set for my class when we first started working with addition & subtraction of fraction with unlike denominators. All of the fractions in the cards’ equations have denominators that allow students to rename just one fraction to match the denominator of the other fraction (e.g. 8/10 + 4/5). This way, you don’t have to worry about students needing to find the least common denominator of two fractions – they simply have to figure out which fraction to rename so that it has the same denominator as the other fraction.

The first 16 cards present equations with unknown sums and differences. The second 16 cards up the challenge level by presenting equations with missing addends, minuends, and subtrahends. [One of the two reference sheets provides a quick review of the vocabulary used to describe the elements of addition and subtraction equations.] In addition, the cards in the second half of the set use a mix of proper and improper fractions.

Included among the printables are two graphic reference sheet. The first of these references is half-page size and presents the terms “added”, “sum”, “minuend”, “subtrahend”, and “difference” in the context of addition and subtraction equations. The second reference sheet is full-page size and walks students through the steps of adding/subtracting fractions when they have different denominators. The example on this reference sheet, like the equations on the cards themselves, uses fractions for which one denominator is a factor of the other, allowing one fraction to be renamed to have the same denominator as the other.

The four provided activity sheets can be used to evaluate student understanding of adding and subtracting fraction with unlike denominators. Two of the activity pages are relatively straightforward, with each containing nine addition and subtraction equations for which the students must find the unknowns. The other two activity sheets are designed to address a student’s reasoning about fraction computation. These two pages present the student with a problem as well as the work and explanation of another student who arrived at the wrong answer. The student is then asked to explain in writing what is incorrect about the reasoning shown.

Ferret-y Fractions

This set is a follow-up to the Foxy Fractions task card set. This set also uses fractions in which one denominator can be renamed to have the same denominator as the other. This set differs from the Foxy Fraction set in that this set uses mixed numbers, and students will either need to regroup the minuend in order to subtract the subtrahend or regroup the sum in order to write it as a proper fraction.

The first 16 cards present equations that use a mixed number and a proper fraction. The equations on cards 1-8 present equations that have an unknown sum or difference, while cards 9-16 up the challenge level by presenting equations with missing addends, minuends, and subtrahends. The second half of the cards (cards 17-32) follow the same format as the first half, but they have equations that use two mixed numbers.

Included among the printables are two handy reference sheets, perfect for your students’ math notebooks. The first of the two graphic reference sheets is half-page size and presents the terms “addend”, “sum”, “minuend”, “subtrahend”, and “difference” in the context of addition and subtraction equations. [NOTE: This reference sheet is nearly identical to one of the reference sheets found in the Foxy Fractions and Fishy Fractions task card sets.] The second reference sheet is full-page size and shows students three different ways that renaming and regrouping can be used to find the difference of a mixed number and fraction with unlike denominators.

The four provided assessment activities can be used to evaluate student understanding of adding and subtracting mixed numbers and fractions with unlike denominators. Two of the activity pages are relatively straightforward, with each containing 9 addition and subtraction equations for which the students must find the unknowns. As with the task cards, all of the equations use fractions with denominators where one denominator is a factor of the other; students only have to rename one fraction to create like denominators. The other two activity sheets are designed to address a student’s ability to analyze solution strategies. These two pages present the student with a problem as well as the work of two students who arrived at the correct answer but used different methods. The student is then asked to compare the two methods.

Fishy Fractions

This Fishy Fractions set primarily uses fractions in which both fractions have to be renamed (such as 3/8 + 1/6 to 9/24 + 4/24) or in which one fraction has to be renamed more than one time (such as 7/12 + 6/9 to 7/12 + 2/3 to 7/12 + 8/12). There are even some equations which can be easily solved by renaming one fraction if the students are savvy about fraction names (for instance, 12/4 – 5/6 to 3 – 5/6). My goal was to provide practice with renaming as a strategy for solving problems while opening up opportunities for multiple ways to work through a problem beyond the standard “find the lowest common denominator” method, which is often, but not always, the most efficient method to add and subtract fractions with unlike denominators.

The first 16 cards in this set present equations with unknown sums and differences. The second 16 cards up the challenge level by presenting equations with missing addends, minuends, and subtrahends. In addition, select cards in each half (cards 9-16 and cards 25-32) use a mix of proper and improper fractions.

Before you have your students work with the cards, you can use one of the included graphic reference sheets as a review of strategies for adding and subtracting with unlike denominators. The first of the two graphic reference sheets is nearly identical to the half-page resource included in the other sets of task cards., while the second reference sheet is unique to this set. It is full-page size and shows students two different ways that renaming can be used to find the sum of two fractions with unlike denominators.

The four provided assessment activities can be used to evaluate student understanding of adding and subtracting fractions with unlike denominators. Two of the activity pages are relatively straightforward, with each containing 9 addition and subtraction equations for which the students must find the unknowns. As with the task cards, all of the equations can be solved by finding the LCD of the fractions, but a number of the fractions were chosen to allow for alternate solution strategies. The other two activity sheets are designed to address a student’s ability to analyze solution strategies, presenting the students with a problem as well as the work of two students who arrived at the correct answer but used different methods and then asking them to compare the two students’ methods.

Self-Checking Puzzles

These seven puzzles progress in difficulty level, providing a level of scaffolding as your students build their proficiency with adding and subtracting unlike denominators and allowing for opportunities to differentiate within the class. The puzzles progress as follows:

• find sum or difference of fractions – only one denominator renamed
• find missing addend, minuend, or subtrahend – only one denominator renamed
• find sum or difference of mixed numbers – no regrouping when subtracted
• find difference of mixed number and fraction – regrouping required
• find sum or difference of fractions – both denominators renamed
• find sum or difference of mixed numbers – both denominators renamed

A list included in the product describes how the difficulty level progresses across the riddles. In addition, the footer on each puzzle identifies the specific skill on which the activity focuses (e.g., adding & subtracting mixed numbers without regrouping). I hope the list will help you in deciding which puzzles are appropriate for your students at a given time of year or for differentiating to meet the varied needs in your class.

There are two versions of the puzzles – one version that does not require any simplifying, with all sums and differences presented in non-simplest form, and another version that requires simplifying. You may opt to use only the puzzles that require simplifying or only the ones that do not require simplifying. Alternately, you can use both versions, having some students complete one and other students complete the other version. Since the two puzzles are virtually identical, your students will have no idea that you are differentiating! The Table of Contents identifies the pages on which you can find the different puzzles.

I Have…Who Has? Cards

This bonus resource – unique to this bundle – contains 2 sets of 32 “I Have, Who Has?” card, labeled as Set A and Set B, as well as master lists of the questions and answer on the two sets of cards.

There are 32 cards 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 much less 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, Set A2, Set B1, and Set B2. 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. The full and half sets are labeled and feature animal icons (a monkey for the full set, an elephant for the first half-set, and a zebra for the second half-set) to easily distinguish the various sets, and a Table of Contents allows you to easily find and print out the exact set you need.

Both Set A and Set B require students to identify the sum or difference of two fractions with unlike denominators. The students are presented with an expression – such as “I have 2/3 + 1/9?” – and they will ask a question about the value of another student’s expression – such as “Who has an expression with a value of 7/12?”. Most of the fractions on the cards are proper fractions, with improper fractions used in some cases; none of the cards use mixed numbers as addends, minuends, or subtrahends. In a number of cases, the sum or difference on the card is a fraction that can be simplified and/or an improper fraction that can be renamed. In these cases, the sum or difference is identified in both forms, so students do not have to be able to simplify or rename – they simply have to be able to rename in order to add or subtract fractions with unlike denominators.

For the pairs of fractions on the Set A cards, one denominator is a multiple of the other, so students need to rename just one of the fractions in order to make like denominators. Set B is more challenging – neither denominator is a multiple of the other, so both fractions have to be renamed in order to add or subtract the fractions.

For more practice with fractions, please check out the other related resources I have available –

Fraction Puzzlers – fraction story problems task cards + printables (set b)

In and Around - area and perimeter task cards + printables (set C)

Name That Equation fraction multiplication task cards + printables set

Fraction Attack – simplifying fraction ppt + printables set

Fraction Matchin’ equivalent fractions task cards + printables (set a)

Monkey Mania & Jumping Giraffes equivalent fractions games + task cards bundle

Flipping for Fractions activity card set

FREE self-checking mixed numeral/improper fraction puzzle set

I hope your students enjoy these resources and are able to build their proficiency with fractions. – Dennis McDonald
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