Students solve problems involving multiplication of two-digit by one-digit numbers and division problems that cannot be solved just by using fact families. They solve multiplication problems by breaking products into the sums of simpler products and write stories that represent their arithmetical processes in a meaningful way. This work leads to the conceptual development of a paper-and-pencil algorithm for multiplication of two-digit by one-digit numbers. Students solve division problems that deal with remainders in various ways and multistep problems that involve both multiplication and division. Students then apply and extend their knowledge of operations using volume as a context. Students solve problems involving volume and measure the volume of containers and objects by counting cubic centimeters, using a graduated cylinder, and by using displacement.
| EXPECTATIONS | |
|---|---|
| Use this list of expectations to assess students on the key concepts and skills in this unit. | |
| E1* | Represent 2-digit by 1-digit multiplication and multidigit division problems using counters, tiles, rectangular arrays, drawings, stories, and number sentences. |
| E2 | Show connections between models and strategies for multiplication (e.g., demonstrate partial products using a rectangle model for multiplication). |
| E3 | Solve multidigit multiplication problems using mental math strategies (e.g., composing and decomposing numbers, and doubling and halving). |
| E4 | Solve multidigit division problems using mental math strategies (e.g., thinking multiplication, repeated subtraction, using turn-around facts). |
| E5 | Multiply one-digit whole numbers by multiples of ten. |
| E6 | Interpret remainders of multidigit division problems. |
| E7 | Solve multiplication problems by breaking products into the sum of simpler products (applying the distributive property of multiplication over addition) using a rectangle model and paperand-pencil methods (e.g., all partials). |
| E8 | Solve multistep word problems involving the four operations. |
| E9 | Use the relationship between larger and smaller units of measure to solve problems. |
| E10 | Measure volume to the nearest cubic centimeter using a graduated cylinder (e.g., through displacement, by filling container). |
| E11* | Estimate volume by counting cubic centimeters. |
| E12 | Find the median of a data set. |
| E13 | Make predictions and solve problems using patterns in data represented in data tables and bar graphs. |
| E14* | Demonstrate fluency with the multiplication facts for the last six facts (4 × 6, 4 × 7, 4 × 8, 6 × 7, 6 × 8, 7 × 8). |
| E15* | Determine the unknown number in a multiplication or division sentence relating three whole numbers for the last six facts (4 × 6, 4 × 7, 4 × 8, 6 × 7, 6 × 8, 7 × 8). |
| E16* | Demonstrate fluency with all the multiplication facts. |
| * Denotes Benchmark Expectation | |