Build your students’ logical reasoning as well as their understanding of multiplicative and additive comparisons with this set of task cards and printables. The 32 task cards in this set will allow your students to practice distinguishing additive and multiplicative comparisons as they work through a series of logic problems. Includes reference material, assessment activities, and even material for differentiating for your high-flyers in need of extension! With these resources, your students will grow stronger in their understanding of a key concept that dominates the Grade 4 Common Core Math Standards for operations & algebraic thinking and lays the foundation for proportional reasoning.
This set of resources is available in a money-saving bundle with three other products that focus on comparative reasoning. The bundle contains three different sets of task cards and printables, a set of five I Have…Who Has?
and accompanying printables, and 2 bonus sets of I Have…Who Has?
cards that are only available in the bundle. Purchase the bundle here
and save 20%
off the cost of the individual products!
Common Core State Standards for Mathematics addressed:
Operations & Algebraic Thinking (4.OA)
• Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (4.OA.2)
• 32 task cards (color and grayscale)
• graphic reference sheet (color and grayscale)
• 2 different answer sheets (keys included for both)
• 2 two-sided activity sheets (scoring guide included)
The printables consist of a graphic reference sheet and two different two-page worksheets. The reference sheet illustrates different comparison – both additive and multiplicative, and describes those comparisons using a variety of academic vocabulary, including double, triple, and quadruple. I have often found that some of my fourth graders have trouble accurately using these terms (sometimes describing 32 as double 64, rather than the other way around), and so I made this to provide a regular reference for terms such as these. 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 multiplicative and additive comparisons.
The 32 task cards in this set (provided in both color and grayscale since each card features graphics) each present students with a logic problem and asks students to interpret a series of clues to find a specific amount. The clues use a mixture of additive and multiplicative comparisons (e.g., Daniel has 3 times as much money as Carrie. Carrie has 4 less dollars than Mike.), requiring students to read carefully to determine whether they need to add/subtract or multiply/divide when interpreting the clues.
The cards in this set scale up in difficulty, allowing students to see success early on and build the strategies and confidence needed to tackle the more complex problems on the later cards. The first 12 cards present problems with 3 clues, the second 12 have four clues, and the final 8 cards have problems with 5 clues. Most of the cards limit the comparisons to single-digit numbers as both factors (or addends), with some the higher-numbered cards adding in the numbers 10, 11, and 12. All the cards follow the same basic format - the first two to four clues describe the relationships between given amounts (weights of dogs, amount of money saved, etc.), the final clue tells the student one of the amounts, and the students are asked a question about a “target amount”. The students then need to go back through the clues, reasoning from one amount to the next, until they are able to figure out the target amount. The cards use varied language when describing the comparative relationships– “fewer than”, “___ times as heavy”, “double”, “more than”, “triple”, etc. – as a means to provide practice with the vocabulary associated with such number relationships.
If your students have a firm grasp on distinguishing between the different types of comparison, you can enrich those students (or extend the practice for all of your students) using the “extension” task card answer sheet. This sheet asks students to identify equations using unknowns to match the first two clues on each card. For instance, if a clue reads, “Mark has 7 less cookies than Nick”, the students may write “M = N - 7” (or M + 7 = N or 7 + M = N or N - 7 = M). This is ideal for students who are ready to begin expressing story problems in a more abstract way, or as a way to revisit this same set of cards later on in the year when your whole class is ready to practice abstract representation of number relationships.
The two provided worksheets can be used to evaluate student understanding of interpreting statements of comparison. The worksheets 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 multiplicative comparison, please check out the other related resources I have available –
Comparison Conundrums math story problems task cards + printables (set a)
Multiplication Madness "I Have...Who Has?" cards + printables set
I hope your students enjoy these resources and are able to build their proficiency with comparative relationships. – Dennis McDonald