3rd Grade Task: Matthew's Dilemma
3rd Grade Task: Matthew's Dilemma
Standards & Objectives
- Recognize area as an attribute of plane figures and understand concepts of area measurement.
- Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- Relate area to the operations of multiplication and addition.
- Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship...
- Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties...
- Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a...
- 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...
- Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g.,...
- Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number...
- Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative...
- Understand division as an unknown-factor problem. For example, find 32 / 8 by finding the number that makes 32 when multiplied by 8.
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 =...
- Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity....
- Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations....
- GLE 0306.1.2
- Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
- GLE 0306.1.3
- Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
- GLE 0306.2.2
- Develop understanding of multiplication and related division facts through multiple strategies and representations.
- GLE 0306.2.3
- Relate multiplication and division as inverse operations.
- GLE 0306.2.4
- Solve multiplication and division problems using various representations.
- GLE 0306.3.1
- Develop meaning for and apply the commutative, associative, and distributive properties using various representations.
- GLE 0306.3.2
- Develop understanding that a letter or a symbol can represent an unknown quantity in a simple mathematical expression/equation.
- GLE 0306.3.3
- Describe and analyze patterns and relationships in contexts.
- SPI 0306.1.5
- Represent problems mathematically using diagrams, numbers, and symbolic expressions.
- SPI 0306.2.5
- Identify various representations of multiplication and division.
- SPI 0306.2.6
- Recall basic multiplication facts through 10 times10 and the related division facts.
- SPI 0306.2.7
- Compute multiplication problems that involve multiples of ten using basic number facts.
- SPI 0306.2.8
- Solve problems that involve the inverse relationship between multiplication and division.
- SPI 0306.3.2
- Express mathematical relationships using number sentences/equations.
- SPI 0306.3.3
- Find the missing values in simple multiplication and division equations.
- SPI 0306.3.4
- Describe or extend (including finding missing terms) geometric and numeric patterns.
- Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of...
- Interpret the factors and products in whole number multiplication equations.
- Interpret the dividend, divisor, and quotient in whole number division equations.
- Multiply and divide within 100 to solve contextual problems, with unknowns in all positions, in situations involving equal groups, arrays, and measurement...
- Determine the unknown whole number in a multiplication or division equation relating three whole numbers within 100.
- Understand division as an unknown-factor problem.
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one...
- Solve two-step contextual problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity....
- Identify arithmetic patterns (including patterns in the addition and multiplication tables) and explain them using properties of operations.
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Essential and guiding questions:
- How are these strategies similar and different?
- Where did you see the numbers in your equaation in the model?
- The first strategy used the relationship between multiplication and division to find the solution. What is the relationship between multiplication and division? Will this strategy work all the time? Explain.
- What do you notice about the product and the dividend? Why are they the same in this problem?
- The second strategy started with 8 x 10 in order to figure out 72 divided by 8. Will this strategy work on all multiplication/division problems?
- The third strategy used the partition model to solve the problem. How is breaking the rectangle apart helpful in solving the problem? Is it possible to partition (break apart) either factor or both? Explain your thinking.
- Which of these strategies work on all multiplication/division problems?
- When do you use multiplication to solve a problem? When do you use division to solve a problem?
Blooms taxonomy level:
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