Are you looking to build your students’ flexibility with numbers? The task cards and printables in this set are the perfect tools for challenge your students to consider number relationships as they interpret addition and subtraction expressions and equations.
Common Core State Standards for Mathematics addressed:
Operations & Algebraic Thinking (5.OA)
Write and interpret numeric expressions.
• Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. (5.OA.2)
• full-page graphic reference sheet
• 32 task cards
• 8 answer cards for self-checking
• task card answer sheet and key
• 4 one-page assessment activities
• key and rubric for assessment activities
I designed these cards to help build my students’ proficiency with interpreting and comparing expressions mentally without actually doing any computation. I found that many of my students could perform calculations accurately but often performed them rotely, using algorithmic procedures even when they were not necessary. I have often seen children mindlessly solve a problem as simple as 17 – 9 by writing the problem vertically, crossing off the 1 and making it a zero, putting a 1 in front of the 7 to make a 17, and then subtract 17-9, without ever once realizing that they were regrouping to create a number that they already had! I needed to build their ability to think more flexibly about addition and subtraction, and so I created these cards to help meet that need. The expressions and equations on these cards use numbers chosen carefully to allow students to use reasoning, rather than pencil and paper computation, to find or compare values.
The printables consist of a graphic reference sheet and four different one-page activity sheets. The graphic reference sheet describes the use of number relationships to interpret expressions and equations without calculating their exact value. Before you have your students complete the cards, you can have them glue the reference sheet in their journals. 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 evaluating expressions and equations.
The 32 task cards present students with a variety of addition and subtraction expressions and equations. The students are asked to use their knowledge of number relationships to compare the expressions or determine the value of unknowns. Along with the 32 task cards are 8 “answer cards”. These answer cards 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.
The four provided worksheets can be used to evaluate your students’ proficiency with using number relationships to interpret and compare expressions. The first two worksheets assess the target concept in a fairly straightforward manner. The other two assessment sheets, however, are designed to assess a student’s ability to critique the reasoning of others, one of the eight Standards for Mathematical Practice. Use these activity sheets as pre- and post-assessments, center activities, guided practice, homework – or any other way that fits your classroom routines or instructional style!
Answer keys are included for the activity sheets. In addition, a rubric is provided to evaluate your students’ written responses to particular questions on the activity pages.
For more practice with number relationships, please check out these other resources I have available –
It's All Relative – multiplication and division number relationships game
Placing the Value - task cards + printables set