Standards
|
Explanations and Examples
|
1. Make sense of problems and persevere in solving them.
|
In third grade, mathematically proficient students know that doing mathematics involves solving problems anddiscussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solveit. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.
|
2. Reason abstractly and quantitatively.
|
Mathematically proficient third graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities.
|
3. Construct viable arguments and critique the reasoning of others.
|
In third grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.
|
4. Model with mathematics.
|
Mathematically proficient students experiment with representing problem situations in multiple ways includingnumbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph,creating equations, etc. Students need opportunities to connect the different representations and explain theconnections. They should be able to use all of these representations as needed. Third graders should evaluate theirresults in the context of the situation and reflect on whether the results make sense.
|
5. Use appropriate tools strategically.
|
Mathematically proficient third graders consider the available tools (including estimation) when solving amathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper to findall the possible rectangles that have a given perimeter. They compile the possibilities into an organized list or a table,and determine whether they have all the possible rectangles.
|
6. Attend to precision.
|
Mathematically proficient third graders develop their mathematical communication skills, they try to use clear andprecise language in their discussions with others and in their own reasoning. They are careful about specifying units ofmeasure and state the meaning of the symbols they choose. For instance, when figuring out the area of a rectangle theyrecord their answers in square units.
|
7. Look for and make use of structure.
|
In third grade mathematically proficient students look closely to discover a pattern or structure. For instance, studentsuse properties of operations as strategies to multiply and divide (commutative and distributive properties).
|
8. Look for and express regularity in repeated reasoning.
|
Mathematically proficient students in third grade should notice repetitive actions in computation and look for moreshortcut methods. For example, students may use the distributive property as a strategy for using products they knowto solve products that they don’t know. For example, if students are asked to find the product of 7 x 8, they mightdecompose 7 into 5 and 2 and then multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. In addition, third graderscontinually evaluate their work by asking themselves, “Does this make sense?”
|