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MATHEMATICS: 4th grade Strategies for Multi-Digit Multiplication
TRAINING MATERIALS NEEDED:
Prepared sets of Digit Cards (2-sets of 0-9 per pair of players) for “Playing with Partial Products”
Copy of large rectangle for each parent
Base ten blocks (units, rods and flats- each parent will need at least 2 flats, 19 rods and 24 unit cubes but don’t give them that exact amount)
RESOURCES FOR PARTICPANT PACKETS:
Powerpoint
Full page learning progression
Large rectangle
Base-ten paper
2 sets of 0-9 digit cards
“Playing with Partial Products” directions and recording sheet
Online resources
CRITICAL POINT:
The purpose of this slide is to welcome parents and share that this session is about how to help their child have a better understanding of the 4th grade standard on strategies for multi-digit multiplication.
STEP-BY-STEP DIRECTIONS:
Welcome Parents and Guardians to the training.
Share that this training is about how they can help their child better understand the 4TH grade standard on strategies for multi-digit multiplication.
Explain that they will be engaged in some activities that will help them better understand the standard and help them support their child with developing their understanding.
The training will also include some purposeful practice tasks that they can do at home.
Only spend about 2 minutes on this slide.

2. What’s the Error? CRITICAL POINT:
Students generalize what they have learned about single-digit multiplication and apply it to multi-digit multiplication by multiplying each column as a separate single-digit multiplication.
CRITICAL POINT:
Engage parents with a task in which they analyze common student misconceptions with the standard algorithm for multi-digit multiplication to give them a purpose for understanding the benefits of the area model.
STEP-BY-STEP DIRECTIONS:
1. Share with participants that this slide is a sample of work from a 4th grader, Sam.
2. Explain that Sam keeps making the same “mistake” when solving 2-digit by 2-digit multiplication problems.
3. Give participants 1 minute to think on their own about what Sam’s misconception is.
4. Give participants another minute or so to share their thinking with a partner.
5. Have participants share out.
6. Click for animation to come in with an explanation of the misconception. Sam is just multiplying the same way he adds, without giving thought to how multiplication is equal groups. It would not be reasonable to say that 34 equal groups of 62 items is only 188.
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3. What’s the Error?
Students misapply the procedure for multiplying multi-digit numbers by ignoring place value.
Students multiply correctly by the ones digit, but ignore the fact that the 3 in the tens place means 30.
CRITICAL POINT:
Continuation of activity from previous slide. Engage parents with a task in which they analyze common student misconceptions with the standard algorithm for multi-digit multiplication to give them a purpose for understanding the benefits of the area model.
STEP-BY-STEP DIRECTIONS:
Share with participants that this slide is a sample of work from a 4th grader, Jon.
Explain that Jon is also struggling when solving 2-digit by 2-digit multiplication problems. He keeps making an error, but his error is different from Sam’s.
Give participants 1 minute to think on their own about what Jon’s misconception is.
Give participants another minute or so to share their thinking with a partner.
Have participants share out.
Click for animation to come in with an explanation of the misconception. Jon is treating each digit as if it is in the “ones”. He is ignoring the place value, which is why he does not include the “place holder” zero.
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4. Mathematics Florida Standards Focus
Grade 4
MAFS.4.NBT.2.5 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit whole 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.
CRITICAL POINT:
Expose parents to the portion of the 4th grade multi-digit multiplication standard that this training will focus on.
STEP-BY-STEP DIRECTIONS:
Share with parents that the misconceptions they just looked at are very common with students who have been rushed to the traditional algorithm and have not been given adequate time to develop a meaningful understanding through experiences with more conceptually based strategies.
Give parents time to read the standard.
Explain that, while the traditional algorithm (the way most adults multiply) is a part of the standard, this workshop will focus on those strategies connected to the distributive property and the illustration of those strategies through arrays/ the area model. These strategies give meaning to multiplication and help prevent misconceptions similar to those we looked at earlier.

5. Multiplication using an Area Model
Learning Progression:
Multiplication using an Area Model
3rd Grade
MAFS.NBT
Multiply one digit whole numbers by multiples of 10, using strategies based on place value and strategies of operations.
4th Grade
MAFS.4.NBT.2.5
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit whole 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.
4th Grade
MAFS.4.NBT.2.5
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit whole 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.
5th Grade
Fluently multiply multi-digit whole numbers using the standard algorithm.
MAFS.5.NBT.2.5
CRITICAL POINT:
This slide shows how learning about multi-digit multiplication progresses from earlier grades to future grades.
STEP-BY-STEP DIRECTIONS:
Give parents time to look at the learning progression. They have a full page version in their packet that might be easier to look at.
Click to advance bring parents’ attention to the 3rd, and 4th grade standards.
Ask parents what they notice about the progression from the 3rd grade standard to 4th grade.
Clarify to help parents see that both standards include utilizing strategies based on place value and the properties of operations, but in 4th grade students will apply their experiences from 3rd grade with multiplying whole numbers by multiples of ten to develop and use strategies based in place value and the properties of operations to multiply multi-digit whole numbers.
Now click to bring up the progression from 4th to 5th grade and ask parents what they notice about the 5th grade standard.
Clarify that it is not until 5th grade that students are expected to be fluent in the traditional algorithm.
Ask parents to think about the conversations we have had up to this point, and share why they think fluency in the traditional algorithm is not until 5th grade.
If needed, clarify that we established in earlier conversations that we do not want to rush to that traditional algorithm. 4th grade is really more focused on those strategies that will deepen students’ conceptual understanding to prevent common errors/misconceptions with the traditional algorithm.
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6. The Distributive Property of Multiplication A multiplication fact can be broken apart into the sum of two different multiplication facts. Example: 3 x 15 = (3 x 7) + (3 x 8) = = 45
CRITICAL POINT:
The purpose of this slide is to give parents a glimpse and brief description of the background knowledge that 4th grade students have from 3rd grade.
STEP-BY-STEP DIRECTIONS:
Tell parents that, for the purpose of the activity that is coming up, they will need to put themselves in the mindset of a 4th grader who has not yet learned multi-digit multiplication.
Share that you will give parents a brief glimpse into some of the background knowledge that a 4th grader would have to draw upon as they make sense of these strategies.
Click to bring up each of the following concepts and give a brief description of each one as they come up:
Array- this is a strategy students used as they were building understanding of the concept of multiplication and as they were working towards basic fact fluency.
Distributive property- this is another strategy that students used to build understanding of multiplication. Students use those facts they already have memorized to help them find the product for those facts they don’t know. This is also known as the “break apart” strategy. This is the primary property that 4th grade instruction will focus on when addressing the part of the standard that refers to
Area- in 3rd grade, students had concrete experiences with area. They would solve for area by counting unit squares, skip counting and using multiplication but the focus was not on the formula.
Multiplying by multiples of 10- in 3rd grade students used their understanding of place value and basic multiplication facts to identify patterns and make sense of multiplying numbers by multiples of ten
Remind parents to keep these concepts in mind during the next activity.
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7. Use base-ten manipulatives to determine the number of unit cubes that will cover the rectangle.
CRITICAL POINT:
Engage parents in an activity to build their conceptual understanding of the connection between place value and multi-digit multiplication and lay the foundation for the area model and partial products. This will also give you the opportunity to assess the parents’ understanding of the base ten blocks.
STEP-BY-STEP DIRECTIONS:
Distribute a copy of the large blank rectangle to each parent.
Pass out base-ten blocks to each parent. Make sure you give them enough so that they have at least 2 flats, 19 rod and 24 unit cubes, but do not give them that exact amount.
Explain to parents that now you are going to take them through some exercises that might be similar to those their students will experience in class as they are using their understanding of place value and properties of multiplication to develop strategies for multi-digit multiplication.
Remind parents to put themselves in the mindset of a 4th grader who has not yet learned the traditional algorithm for multi-digit multiplication.
Task parents with using the base ten blocks to find out how many unit cubes it would take to cover the entire rectangle.
If you see that parents are really, REALLY struggling because they see that they do not have enough of the actual unit cubes to cover the rectangle, you may need to do a quick mini-lesson on base-ten blocks and explain that these are tools used to represent the relationship between place values. For this activity, and for most experiences with whole numbers, the unit cube has a value of 1, the rod has a value of 10 and the flat has a value of Parents most likely will not know the terms “rod” and “flat”, so you will want to clarify that we use these names for the tools, because the value of each block can be changed to represent different magnitudes of numbers. For example, later in the year, 4th graders will use the same blocks to represent decimals place value, but then the flat will have a value of 1, the rod will be one-tenth and the unit cube will be one-hundredth.
Give parents 5 minutes to work with a partner to complete the task.
While they are working, walk around and look for the different strategies parents are using. Look specifically for models that group together flats, rods and the units- you want to share those strategies that are closest to the picture on the next slide. Listen for strategies that include the use of place value.
You may need to remind parents that they should not be using the traditional algorithm at any point (we anticipate some parents will just find the length and width of the rectangle and use that traditional algorithm to multiply).
Based on what you observed while walking around, select one or two parents to share their strategy for covering the rectangle. While they are sharing, restate using place value vocabulary where appropriate.
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8. = 414 Efficient Solution: 18 23 10 10 x 3 = 30 10 x 20 = 200 8 10 8
10 x 20 = 200
8 x 20 = 160
10 x 3 = 30
8 x 3 = 24
= 414 18
CRITICAL POINT:
Make connection between the previous “covering” activity and partial products strategies.
STEP-BY-STEP DIRECTIONS:
You may or may not have had a parent create a model like the one that is on this slide. If you did not, you will want to explain that this is an efficient way we could have covered the rectangle and it would be efficient for finding the total amount units, because you can skip count by place value to find the total.
Ask parents what the dimensions would be of the rectangle. ( 23 x 18)
Click for the dimensions to appear.
Remind parents that standard really focuses in on using strategies that are rooted in place value and properties of multiplication (specifically, we are focusing in on the distributive property, or breaking apart numbers).
Click to show breaking apart the model into smaller arrays and breaking apart the dimensions.
Share that by breaking apart dimensions by place value and breaking apart the array into smaller arrays, we were able to reduce the computation to problems in which we can use what we know about basic facts and multiplying by multiples of ten to find parts of our total product, or “partial products”.
Click to show the equations with each partial product. Re-iterate that by breaking apart the multiplication problem by place value into these smaller problems, we used were able to use skills from the 3rd grade standards to find the partial products.
Ask parents how they think they could use the partial products to find the total product (414) of the dimensions. (They can add the partial products together to get the final product).
Tell parents that they have paper versions of the base ten blocks in their participant packets if they would like to use them with their child at home.

9. Using the model below, how could you represent the following multiplication problem?
18 x 23 20 3 10
10 x 20 = 200
10 x 3 = 30
= 414
CRITICAL POINT:
Explore the more efficient area model for visually representing the breaking apart of factors for multi-digit multiplication.
STEP-BY-STEP DIRECTIONS:
Explain to parents that making sense of multi-digit multiplication through the use of base-ten models is necessary for building the foundation of understanding multi-digit multiplication and teachers will devote a significant amount of time to this. However, we do want students to move towards more efficient strategies.
Show parents the open area model. Explain that this area model is a more efficient way for students to illustrate their use of the distributive property to find partial products.
Give parents 1-2 minutes to identify the values that would complete the illustration, including the factors, partial products and final product.
Have parents share their solutions. Restate the steps the parents share using place value vocabulary where appropriate. 8
8 x 20 = 160
8 x 3 = 24
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10. The Distributive Property of Multiplication
MAFS.4.NBT.2.5
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit whole 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.
The Distributive Property of Multiplication
A multiplication fact can be broken apart into the
sum of two different multiplication facts.
CRITICAL POINT:
Explore the written record for partial products.
STEP-BY-STEP DIRECTIONS:
Explain that while it is not necessarily more efficient, the written record for partial products is the next step after students understand the area model, and it is still connected to place value. This strategy will help students understand why the traditional algorithm works when we get there.
This slide shows the area model for 23 x 18 next to a version of a written record for partial products. Ask parents to look for connections between the two strategies.
Parents should see that with the written record the factors are still being broken apart by place value, and we are finding the sums of the partial products just like on the area model.
Click to bring up the example of the distributive property for this problem with the definition of that property.
Ask parents how this way of recording connects to the area model and partial products. They should see that the smaller multiplication problems are grouped using parenthesis.
Click to bring up the standard, and ask parents to think about how these three strategies connect to the standard.
Clarify that all three strategies are connected to place value and that the area model and partial products are really just more concrete ways of modeling the distributive property. The area model is a way to illustrate both partial products and the distributive property.
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11. MAFS.4.NBT.2.5
Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit whole 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.
CRITICAL POINT:
Share a sample of student work demonstrating understanding of the standard.
STEP-BY-STEP DIRECTIONS:
Draw parents’ attention back to the standard.
Share with them an example of a task that might be used to assess a student’s understanding of the standard.
Specifically, this task shows how a student might record using partial products.
Ask parents what they notice about the students’ work. They should see that this student’s written record of partial products is not recorded exactly the way that we looked at recording partial products. Clarify that this does not matter; based on this student’s work, we can see evidence of breaking apart the factors by place value to find partial products. It is evident that this student does not just follow a set of memorized procedures, but uses their understanding of the distributive property (breaking apart problems into simpler problems) and place value to find the partial products.
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12. DO TRY THIS AT HOME! Take it Home and Try It!
Warning: Implementing this engaging activity will result in an increase in motivation and long-lasting learning.
CRITICAL POINT:
Parents practice game they can play at home to reinforce the standard.
STEP-BY-STEP DIRECTIONS:
Refer parents to the “Playing with Partial Products” directions, recording sheet and digit cards in their packet.
Give parents some time to play the game.
The amount of time that you give parents to play will depend on the amount of time left in the training.
Remind parents that they can provide their child with the paper models of the base ten blocks if they need additional support when solving for the products at home.
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13. Online Resources The Amoeba Multiplication Game:
Partial products video:
Multiplying 2-digit by 2-digits with Area Models:
CRITICAL POINT:
Share with parents some online games, practice, and instructional videos that could help reinforce this standard.
STEP-BY-STEP DIRECTIONS:
If there is time and you have internet access, visit some of these websites.
Address any additional questions parents may have.
Thank parents for coming.
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