Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
[divider] [/divider] Students are able to…
- Make connections between models, drawing and strategies to written equations.
- Use place value when decomposing numbers within multiplication.
- Use a variety of strategies to solve and explain their reasoning.
- Determine if the answer is reasonable using mental math, rounding or estimation.
[divider] [/divider] Students are able to…because teachers:
- Promote the use of visual models to show their understanding.
- Pose problems that allow for various solution strategies.
- Facilitate discussion and ask questions that connect models to equations and algorithms.
- Provide exposure to multiple strategies that can be used to solve multiplication problems.
[divider] [/divider] Questions to ask students:
- Can you describe/identify a situation in which you would need to multiply two numbers?
- Sample answer that indicates understanding: Student gives a problem solving scenario that deals with knowing the number of equal groups and numbers in each group, but are needing to determine the total.
- How can you use the basic fact 6 x 7 to help you determine the product of 6 x 700?
- Sample answer that indicates understanding: I know that the basic fact of 6 x 7 = 42. If 6 x 7 = 42, 6 x 70=420, and 6 x 700=4,200. It increase the product by 100 times so there are two more zeroes added to the end of the basic fact.
- Will the product of 27 x 9 be less than or greater than 300? How do you know?
- Sample answer that indicates understanding: I know that 30 x 10 would be 300, and both factors are less than those. So the product has to be less than 300.
- Sample answer that indicates an incomplete understanding or a misconception: I don’t know until I write it down and figure it out.
- Sample answer that indicates understanding: I know that 30 x 10 would be 300, and both factors are less than those. So the product has to be less than 300.
- In the problem 34 x 70, why is there a zero in the ones place of the product?
- Sample answer that indicates understanding: The zero is at the end of the product because I’m multiplying by 7 tens, not just 7. My answer would be 10 times greater than if I was multiplying by 7.
- Sample answer that indicates an incomplete understanding or a misconception: I added a zero to the end of my answer because anything times 0 is 0.
- Looking at your area model for the problem 27 x 6, explain how you decomposed the factors. How did that help you solve the original problem?
- Sample answer that indicates understanding: I broke the factors apart by place value. Then I was able to multiply using partial products, basic facts and place value.
- How could you use partial products or the distributive property of multiplication to help you solve 67 x 23?
- Sample answer that indicates understanding: First I would break apart the 67 into 60 + 7, then break apart 23 into 20 + 3. I could then multiply 60 x 20, 60 x 3, 7 x 20, 7 x 3. Then I would add those amounts to determine the product of 67 x 23.
[divider] [/divider] FSA Notes
Cognitive Complexity Level: 2 – Basic Application of Skills and Concepts
Achievement Level Descriptors:
2- multiplies a whole number (of up to three digits) by a single-digit whole number, including the use of strategies based on place value and visual models
3- multiplies a whole number up to four digits by a single-digit whole number and two two-digit whole numbers, using strategies based on place value; illustrates and explains calculations by using equations, rectangular arrays, and/or area models
4- determines the equation that represents a base-ten model; makes connections between different multiplication strategies
5- analyzes and describes an error in a strategy and shows the correct solution
Assessment Limits:
Items may require multiplying: four digits by one digit, three digits by one digit, two digits by one digit, or two digits by two digits.
Context: No Context
[divider] [/divider] Additional Resources:
Additional in depth content knowledge
The Progression of Multiplication
Connecting Academics and Parents- 4th Grade Multi-Digit Multiplication
Video: Solve 2 by 2 digit multiplication problems: using partial products
[divider] [/divider] Sample Formative Assessment Tasks:
Resources/Tasks to Help Your Child at Home:
Roll a Dice to determine the two basic facts. Roll again to determine how many zeroes go behind each of the factors. Using basic facts to determine the product of the original factors. Then determine how the basic fact will relate to the action product. Example: I roll a 2 and a 7. Then I roll a 2 and a 2. My problem is 200 x 700. The basic of 2 and 7 is 14. Because I’m multiplying 200 x 700, I will need to add 4 zeroes behind the basic fact. The answer is 200 x 700 = 140,000.
Khan Academy: Multiply 1 digit numbers by Multiples of 10, 100, and 1000 https://goo.gl/85tPuk
As your child is solving different multiplication problems, have them use at least 2 strategies (base ten model, array model, partial products box model, partial products or place value multiplication. Ask questions such as:
- How do the 2 strategies relate?
- How does your model relate to the problem?
- Where do you see the area model in the partial products box model?
Khan Academy: Multiplying with Area Model 16 x 27 https://goo.gl/mbgoKw
Khan Academy: More Ways to Multiply https://goo.gl/8Pp6AA
Using a deck of cards, create a 2-digit by 1-digit. Choose another card for your 1-digit number. Find the product of the two factors by using an area model and then partial products. Continue with 3-digit by 1-digit, 4-digit by 1-digit problems also. Record the new problem as a distributive property equation.
Khan Academy: Multiplying with the Area Model 6 x 7,981 https://goo.gl/ZxZ7Hs
Using a deck of cards, create a 2-digit by 2-digit number. Find the product of the two factors by using an area model and then partial products. Record the new problem as a distributive property equation.
Khan Academy: Multiplying with the Distributive Property https://goo.gl/eRo89p