Operations and Algebraic Thinking Tasks

Featuring Tasks from Illustrative Mathematics

Kindergarten: K.OA.2

Show the student 6 counters (small, flat objects). Ask the student to close his/her eyes. Hide some of the counters under a sheet of heavy paper. When the student opens his/her eyes, s/he determines how many were hidden based on the number of counters still showing.

Repeat the task 4-5 times per student.

This task may be repeated with a different number of counters.

Students should eventually be able to recognize the number of counters that are showing and/or hidden without counting.

IM Commentary: "The words compose and decompose are used to describe actions that young students learn as they acquire knowledge of small numbers by putting them together and taking them apart. This understanding is a bridge between counting and knowing number combinations. It is how instant recognition of small numbers develops and leads naturally to later understanding of fact families."

Grade 3: 3.OA.3

Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend?

Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy?

Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get?

Solve using a tape diagram.

IM Commentary: "The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group? Sometimes the second type of problem is referred to as a measurement division or repeated subtraction problem. The third type of problem is sometimes called a partitive division or sharing problem. It asks how large is each share when a whole is divided equally into a specified number of pieces. It specifies the size of each share and asks how many of that size are in the whole. The language used in the solution reflects the language in the common core, which also refers to them "Number of Groups Unknown" or "Group Size Unknown," respectively." It is important for students to see all three types of problems.

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