Question

chapter learning target: understand multiplying by two - digit numbers. chapter success criteria: i can estimate a product of two numbers. i can use an area model to multiply. i can use partial products to multiply. i can use regrouping to multiply. surface deep chapter review rate your understanding after each section. 3.1 multiply by tens learning target: use place value and properties to multiply by multiples of ten. find the product. 1. 50×20 = 1000 2. 30×60 = 1800 3. 18×30 = 540 3.2 estimate products learning target: use rounding and compatible numbers to estimate products. estimate the product. 4. 25×74 5. 16×28 6. 42×81 3.3 use area models to multiply two - digit numbers learning target: use area models and partial products to multiply. 7. draw an area model to find the product. 13×19 = __ 8. write the multiplication equation represented by the area model. 20 400 80 8 160 32 × = __

Explanation:

Step1: Estimate 25×74

Round 25 to 25 (it's already a convenient number) and 74 to 70. Then multiply: 25×70 = 1750.

Step2: Estimate 16×28

Round 16 to 20 and 28 to 30. Then 20×30 = 600.

Step3: Estimate 42×81

Round 42 to 40 and 81 to 80. Then 40×80 = 3200.

Step4: Calculate 13×19 using area - model concept

13 = 10 + 3 and 19 = 10+9.
The area - model has four parts: 10×10 = 100, 10×9 = 90, 3×10 = 30, 3×9 = 27.
Sum them up: 100 + 90+30 + 27=247.

Step5: Analyze the given area - model

The side lengths of the rectangle seem to be 28 (20 + 8) and 28 (20 + 8) since 20×20 = 400, 20×8 = 160, 8×20 = 160 (not shown separately but part of the model concept), 8×8 = 64 (but we have 80 and 32 which are likely mis - labeled or part of a different way of splitting). If we assume the correct numbers based on the model structure, the equation is 28×28=784.

Answer:

1. Estimate: 1750
2. Estimate: 600
3. Estimate: 3200
4. 247
5. 28×28 = 784