A set of 20 open-ended problem solving task cards covering a range of mathematical concepts.

These open-ended problem solving task cards will promote deep, thoughtful, and creative responses from your students. More than one answer is acceptable; exploring possibilities is encouraged.

The problems cover a range of mathematical concepts such as place value, number operations, measurement, combinations, and data analysis.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol...

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - ...

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it wi...

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite sha...

Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 o...

Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × ...

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph i...

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangl...

Use a problem-solving model that incorporates
analyzing given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques,
including mental math, estimation,
and number sense as appropriate, to solve
problems;

Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including
symbols, diagrams, graphs, and language as appropriate;

Use objects and pictorial models to solve
word problems involving joining, separating, and comparing sets within 20
and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3;

Identify two-dimensional shapes, including circles, triangles, rectangles,
and squares, as special rectangles, rhombuses, and hexagons and describe their
attributes using formal geometric language;

Use a problem-solving model that incorporates
analyzing given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques,
including mental math, estimation,
and number sense as appropriate, to solve
problems;

Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including
symbols, diagrams, graphs, and language as appropriate;

Use concrete and pictorial models to compose and
decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones;

Use a problem-solving model that incorporates
analyzing given information, formulating a plan or strategy, determining a solution,
justifying the solution and evaluating the problem-solving process and the reasonableness of the solution;

Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques,
including mental math, estimation,
and number sense as appropriate, to solve
problems;

Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including
symbols, diagrams, graphs, and language as appropriate;

Compose and decompose numbers up to 100,000
as a sum of so many ten thousands, so many thousands, so many hundreds, so many
tens, and so many ones using objects, pictorial models, and numbers, including
expanded notation as appropriate;

Solve with fluency one-step and two-step
problems involving addition and subtraction within 1,000 using strategies based
on place value, properties of operations, and the relationship between addition
and subtraction;

Represent multiplication facts by using
a variety of approaches such as repeated addition, equal-sized groups, arrays,
area models, equal jumps on a number line, and skip counting;

Use attributes to recognize rhombuses, parallelograms,
trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples
of quadrilaterals that do not belong to any of these subcategories;

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