Multiplying Two Digit by One Digit Numbers with Regrouping
Description: A problem context of shopping and buying items is used.
Purpose: to help students make meaningful connections between what they have experienced with shopping and spending money and the skill of multiplying two digit by one digit numbers with regrouping.
Learning Objective 1: Use concrete objects to solve two digits by one digit multiplication problems with regrouping.
Materials:
Teacher –
3 groups of Baseball cards
Description:
1.) L ink to students’ prior knowledge of using multiplication to figure out problems.
For Example:
How many of you like to shop? When we shop we need to decide what we want to buy. We also need to decide how many we need or want to buy. Suppose you went to a grocery store with your mom and she told you that you could get 3 packs of Baseball cards. (Show packs of cards). Each pack had 15 cards. If you get 3 packs of 15 cards, how many cards will you have all together? Hmm. – That sounds like a multiplication problem to me. We have 3 packs of cards that have 15 cards each.
2.) I dentify the skill students will learn.
For Example:
We’ve been working on multiplication. We have worked on multiplying tens (show example of abstract problem with corresponding concrete and representational display) and we have worked on multiplying two digits by one digit numbers like this (show example of abstract problem with corresponding concrete and representational display). You have done so well solving these problems that today we are going to start working on some tougher multiplication problems. When we do these problems, we will need to make sure that we pay close attention and regroup when we need to. Each of these problems will involve regrouping. To help us start solving problems like this we are going to use our base ten blocks and our place value mats.
3.) P rovide rationale/meaning for solving two digit by one digit multiplication problems with regrouping.
For Example:
Knowing how to do problems like this will help us when we need to multiply larger numbers. It will help you when you shop to decide how many of each thing you want to get and how many you have all together.
Purpose: to provide students a clear teacher model of how to solve two digits by one digit multiplication problems with regrouping using concrete materials.
Learning Objective 1: Use concrete objects to solve two digits by one digit multiplication problems with regrouping.
Materials:
Teacher –
Base ten blocks, ten sticks, place value mat,
String or yarn
Description:
A. Break down the skill of multiplying two digits by one digit numbers with regrouping using concrete objects.
1.) Identify numbers/factors in problem.
2.) On place value mat, show the number of groups.
3.) On place value mat, show number of items/group.
4.) Count blocks in the ones column.
5.) Trade groups of ten for ten sticks.
6.) Count blocks left in the ones column.
7.) Count ten sticks in the tens column.
8.) Say the number that is shown.
9.) Repeat the multiplication problem.
Purpose: to provide students an opportunity to build their initial understanding of how to multiply one digit by two digit numbers with regrouping using concrete objects and to evaluate your students’ levels of understanding after you have initially modeled the skill.
* The following description is for Learning Objective 1: Use concrete objects to solve two digits by one digit multiplication problems with regrouping.
Materials:
Teacher –
Base ten blocks, ten sticks, place value mat
Visual display area
Students 
Base ten blocks, ten sticks, place value mat
Description:
1.) Scaffold Using a High Level of Teacher Direction/Support
a. Choose one or two places in the problemsolving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction. (Examples of choices are shown in red.)
Identify number/factors in problem
We have been working on multiplication problems involving regrouping. This time, I am going to work a problem and I want you to help me with part of it. If I went shopping and bought 6 packs of cards and each pack had 12 cards in it, I wonder how many cards I would have in all? I need to figure out a couple of things. The first thing I need to do is see which number stands for how many groups I have. What do you think? How many groups do I have? You are right, I have 6 packs of cards, so I have 6 groups. Now that is my number of groups, but I need another number, I need to know how many items I have in each group. What do you think is that number? Right, 12, because I have 12 cards in each pack. So I have how many packs? And how many cards in each pack?
On the place value mat, show the number of groups
I am going to use yarn to make the number of groups on my place value mat. How many groups should I make? Right 6. I am going put down 6 pieces of
yarn across my place value mat.
On place value mat, show the number of items/group using base ten blocks and ten sticks.
Now I need to show how many cards are in each pack. There are 12 cards in each pack. I need to see how many ones are in the number 12. Show me how many ones are in 12. Right, there are 2 ones. How many tens are in 12? Right again, there is one ten. I can show 12 with 2 blocks and 1 ten stick. Well, we know that we have 12 cards in each pack,. What should I put in each group here on my place value mat? Right, I am going to put 12 in each group. ___ and ____, how do I make 12? You are right; we can show 12 with 2 blocks and 1 ten stick. I am going to put 2 blocks and 1 ten stick here in this group, and in this group, …. There I have made 12 in each group on my place value mat.
Count the number of blocks in the ones column of the place value mat.
I have made 6 groups of 12. I want to see how many I have all together. Where should I start counting? Right, in the ones column. I will start counting here. 1,2,3,4,5,6,7,8,9,10. Now I have 10 blocks in the ones column. I think I need to do something. What should I do? Right, I need to make groups of 10.
Trade groups of ten for ten sticks and place the ten sticks in the ten column of the place value mat.
I need to take this group of ten blocks from the ones column and trade it in for a ten stick. Should I move my ten stick out of the ones column? Yes, I need to put my ten stick at the top of my tens column like this.
Count blocks left in ones column
Now I need to count my blocks in the ones column. Can I make any more groups of 10? No, I can’t. I have 2 blocks left in my ones column.
Count ten sticks in the tens column
I’ve counted my ones, now what should I do? Right, I need to count my tens. I have 1,2,3,4,5,6 sticks in my tens column (point to sticks) plus one more that I move over (point to stick at top of tens column). How many total ten sticks do I have? Right 7.
Say the number that is represented on the place value mat.
How many tens do I have? Seven tens are what? Right 70. Plus 2 ones (point to ones) makes 71, and 72. I have 72 blocks in all.
Repeat the multiplication problem, saying the answer that is shown by the concrete materials on the place value mat.
Now I know the answer to my problem. If I buy 6 packs of cards and each pack has 12 cards in it, how many cards will I have all together? Right 72 cards. Six times 12 is 72.
b. Maintain a high level of teacher direction/support for another example if students demonstrate mis../../../understanding/nonunderstanding; move to a medium level of teacher direction/support if students respond appropriately to the selected questions/prompts.
2.) Scaffold Using a Medium Level of Teacher Direction/Support
a. Choose several more places in the problemsolving sequence to invite student responses. Have these choices in mind before you begin scaffolding instruction.
Identify number/factors in problem
You are doing a great job figuring out these problems. This time, I ‘m going to ask for even more of your help. Let’s say that we have 3 bags of suckers and each bag has 14 suckers in it. We want to find out how many suckers we have all together.. The first thing we need to do is see which number stands for the number of groups. What do you think? How many groups do we have? Why do you think that? You are right, we have 3 bags,so we will have 3 groups. Now that is our number of groups, but we need to know something else. We need to know how many items we have in each group. What do you think is that number? Right, 14, because I have 14 suckers in each package. So I have how many packs? And how many cards in each pack?
On the place value mat, show the number of groups
What should I do first on my place value mat? Right, I need to use yarn to make the number of groups on my place value mat. How many groups should I make? Right 3. Why 3? Because we have 3 bags of suckers. I am going put down 3 pieces of yarn across my place value mat.
On place value mat, show the number of items/group using base ten blocks and ten sticks.
Now that we’ve shown our groups, what should we do next? You are right, we need to show how many suckers are in each bag. There are 14 suckers in each bag. We need to see how many ones are in the number 14. Show me how many ones are in 14. Right, there are 4 ones. How many tens are in 14? Right again, there is one ten. ___ and ____, would you please come show me 14 using the ten blocks and ten sticks? We can show 14 with 4 blocks and one ten stick. Now we need to show how many items are in each group on our place value mat. _____ show me what we are going to put in the first group. Is he right boys and girls? Great! ______, show me what we are going to put in our second group. How about it, did she do it correctly? We are on a roll. ____, what should we put in our third group? Right, we are going to put 4 one blocks and one ten stick to show that we have 14 in this group also. ____, There, we have made 14 in each group on the place value mat.
Count the number of blocks in the ones column of the place value mat.
We have made 3 groups of 14, and we want to see how many we have all together. _______, where should we start counting? Right, in the ones column. ____ and ______, please count the ones for us. They counted 12. Is there anything they need to do? Right, they need to trade a group of 10.
Trade groups of ten for ten sticks and place the ten sticks in the ten column of the place value mat.
_____ and _______, show us what to do with this group of 10 in the ones column. Great, they took the ten ones and traded it for a ten stick. Where should that ten stick go? Right, at the top of the tens column.
Count blocks left in ones column
____ and ____, how many blocks do we have left in the ones column?
Count ten sticks in the tens column
_____, what should we do next? Right, we count our ten sticks. How many ten sticks do we have? How did you get that number? Right, you counted the number of ten sticks we have in our tens column (1,2,3) and then added one more that we put at the top when we traded. So 3 tens plus 1 ten is 4 tens.
Say the number that is represented on the place value mat.
______ and _______, can you tell us what number we have shown on our place value mat? Boys and girls, they said we have 42. How many tens do we have? And 4 tens are what? Right 40. Plus 2 ones (point to ones) makes 41, and 42.
Repeat the multiplication problem, saying the answer that is shown by the concrete materials on the place value mat.
Boys and girls, what is the answer to our problem? 14 x 3 is 42 suckers.
b. Maintain a medium level of teacher direction/support for another example if students demonstrate mis../../../understanding/nonunderstanding; move to a low level of teacher direction/support if students respond appropriately to the selected questions/prompts.
3.) Scaffold Using a Low Level of Teacher Direction/Support
a. When students demonstrate increased competence, do not model the process. Ask students questions and encourage them to provide all responses. Direct students to replicate the process at their desks as you work together.
Identify number/factors in problem
Let’s try another problem. This time, I want you to work at your desks using the base ten blocks and place value mats. I’ll work one up here while you work it at your desks. The fourth graders are going to have an ice cream sundae party. We have 3 boxes of plastic spoons and each box holds 15 spoons. We need to see how many spoons we have all together. How many groups do we have? Right, 3. What is the other number we will be working with? Right, 15 because there are 15 spoons in each box.
On the place value mat, show the number of groups
What should I do first on my place value mat? Right, I need to use yarn to make the number of groups on my place value mat. How many groups should I make? Right 3. Why 3?
On place value mat, show the number of items/group using base ten blocks and ten sticks.
Now that you each have 3 groups on your mat, what should you do next? You are right, we need to show the number of spoons. On your place value mat, show me the number of spoons in each box. What number did you show in each group on your place value mat? ____, and _____, could you please come show us on my place value mat.
Count the number of blocks in the ones column of the place value mat.
What should we do next? Right, we need to count. ______, where should we start counting? Right, in the ones column. How many ones do you count? Do you need to do anything with these ones?
Trade groups of ten for ten sticks and place the ten sticks in the ten column of the place value mat.
Show me what to do with the ones in the ones column. _____ , please tell me what to do on my place value mat. Okay, I take ten ones and I trade them in for a ten stick. Show me where should that ten stick go.
Count blocks left in ones column
Tell me how many blocks you have left in the ones column?
Count ten sticks in the tens column
What should we do next? How did you get that number? _____ , please come show me what to do on my mat.
Say the number that is represented on the place value mat.
What number do you have on our place value mat? Tell me what number I have. I have ____ tens, which makes _____, plus ____ ones, so I have _____.
Repeat the multiplication problem, saying the answer that is shown by the concrete materials on the place value mat.
Boys and girls, what is the answer to our problem?
b. When you are confident students understand, ask individual students to direct the problem solving process or have the class direct you: Students ask questions and you and the students respond/perform the skill.
Purpose: to provide students multiple practice opportunities to recognize the correct answer for two digits by one digit multiplication problems with regrouping.
Learning Objective 1: Use concrete objects to solve two digits by one digit multiplication problems with regrouping.
Cooperative Learning
Materials:
Teacher –
Bell or timer
5 problem cards, along with materials that represent each problem
Sheet/chart to record team scores
Students 
Each team will need 5 place value mats with base ten blocks and ten sticks displayed on mat (You may want to laminate the mats and hot glue or velcro the materials to keep them from rolling off. Alternatively, you could place each mat in a box lid to help secure it.) Each place value mat should be numbered (15).
Description:
Activity:
Children will work in groups of 4 or 5 students. Each table will have 5 place value mats that are numbered and have base ten materials on them. The teacher will choose a problem 15. . Each team is to look at the correspondingly numbered place value mat and decide if it shows the correct solution to the problem that the teacher presents. After the teacher rings the bell, one member of each team will announce their decision. Teams can earn points for each correct decision.
Cooperative Learning Groups Steps:
1.) Provide explicit directions for the cooperative group activity including what you will do, what students will do, and reinforce any behavioral expectations for the game.
2.) Arrange students in cooperative groups. Groups should include students of varying skill levels.
3.) Assign roles to individual group members and explain them:
a. Materials manager (gets the materials – sets of place value mats)
b. Time Keeper (makes sure that each student at the table gets a chance to share in time allotted)
c. Reporter (reports group’s answer)
d. Encourager(s) (encourages each person)
4.) Distribute materials.
5.) Model one example of skill(s).
a. Listen to problem.
b. Look at corresponding place value mat.
c. Decide if mat shows solution to problem.
d. Make sure that the team agrees with the decision before time is called.
6.) Review/model appropriate cooperative group behaviors and expectations.
a. Agree or disagree with a teammate’s decision.
b. Listen while teams are sharing responses.
7.) Provide opportunity for students to ask questions.
8.) Teacher monitors and provides specific corrective feedback & positive reinforcement.
a. Circulate around the tables and check on children’s responses.
b. Make sure that each child receives feedback on his/her decision.
c. Ask each child in the class to share his/her decisions at least once either with the entire class or individually with the teacher.
Purpose: to provide students multiple practice opportunities to solve two digit by one digit multiplication problems with regrouping using concrete objects.
Learning Objective 1: Using concrete objects. to solve two digit by one digit multiplication problems with regrouping.
Cooperative Learning
Materials:
Teacher –
Bell or timer
5 problem cards, along with materials that represent each problem
Sheet/chart to record team scores
Students 
Place value mat/team
Base ten blocks and ten sticks/team
Description:
Activity:
Children will work in groups of 4 or 5 students. Each table will have a place value mat and base ten materials on them. The teacher will choose a problem 15. . Each team is to show the solution on the place value mat. After the teacher rings the bell, one member of each team will share their solution. Teams can earn points for each correct decision.
Cooperative Learning Groups Steps:
1.) Provide explicit directions for the cooperative group activity including what you will do, what students will do, and reinforce any behavioral expectations for the game.
2.) Arrange students in cooperative groups. Groups should include students of varying skill levels.
3.) Assign roles to individual group members and explain them:
a. Materials manager (gets the materials – sets of place value mats)
b. Time Keeper (makes sure that students are on task and complete each problem in time allotted.)
c. Turn taker (makes sure that each member of the group gets a chance to solve a problem)
d. Encourager(s) (encourages each person)
4.) Distribute materials.
5.) Model one example of skill(s).
a. Listen to problem.
b. Show solution
c. Make sure that the team agrees with the decision before time is called.
6.) Review/model appropriate cooperative group behaviors and expectations.
a. Agree or disagree with a teammate’s decision.
b. Listen while teams are sharing responses.
7.) Provide opportunity for students to ask questions.
8.) Teacher monitors and provides specific corrective feedback & positive reinforcement.
a. Circulate around the tables and check on children’s responses.
b. Make sure that each child receives feedback on his/her decision.
c. Ask each child in the class to share his/her decisions at least once either with the entire class or individually with the teacher.
Purpose: to provide you with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a way to visualize their learning/progress.
Materials:
Teacher –
Appropriate prompts if they will be oral prompts
Appropriate visual cues when prompting orally
Student
Appropriate response sheet/curriculum slice/probe
Graph/chart
Description:
Steps for Conducting Continuous Monitoring and Charting of Student Performance:
1.) Choose whether students should be evaluated at the receptive/recognition level or the expressive level.
2.) Choose an appropriate criteria to indicate mastery.
3.) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.
a. Based on the skill, your students’ learning characteristics, and your preference, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with appropriate prompts), or oral in nature with visual cues (ask students to tell you which of several visually displayed solutions is the correct solution for a problem), or a combination of written curriculum slices/probes and oral prompts with visual cues (e.g. ask students to demonstrate solution to given oral problem).
4.) Distribute to students the curriculum slice/probe/response sheet/concrete materials.
5.) Give directions.
6.) Conduct evaluation.
7.) Count corrects and incorrects/mistakes (you and/or students can do this depending on the type of curriculum slice/probe used – see step #3).
8.) You and/or students plot their scores on a suitable graph/chart. A goal line that represents the proficiency (for concrete level skills, this should be100% or 5 out of 5 correct) should be visible on each student's graph/chart).
9.) Discuss with children their progress as it relates to the goal line and their previous performance. Prompt them to selfevaluate.
10.) Evaluate whether student(s) is ready to move to the next level of understanding or has mastered the skill at using the following guide:
Concrete Level: demonstrates 100 accuracy% (given 3 to 5 tasks) over three consecutive days.
11.) Determine whether you need to alter or modify your instruction based on student performance.
Flexible Math Interview
Purpose: to provide you with additional diagnostic information in order to check student understanding and plan and/or modify instruction accordingly.
Materials:
Problem bags – bags with packages of gum, cookies, cards, etc.
Place Value Mats,
Base ten materials
Description:
With individual students or in small groups, the teacher will take the role of a student. After drawing a “problem bag”, the teacher will have the student teach him/her how to solve the problem using the place value mats and base ten materials. The teacher should note errors and/or misconceptions while the student is teaching, but the teacher should not stop the student for correction purposes. By having the student complete the entire explanation, the teacher will gain a better understanding of the student’s thinking. The teacher should confer with the student regarding specific errors or misconceptions after the activity is over.
Purpose: to provide periodic student practice activities and teacher directed review of this skill after students have mastered it.
1. Problem of the Day
Materials:
Concrete objects that depict a problem (e.g. 4 packs of 12 pencils).
Place value mats,
Base ten materials
Description:
The teacher will present a problem of the day verbally and by displaying the items in a designated area. Students will solve using base ten materials and place value mats. This should initially be done each day, then 2 times/week, weekly, bi weekly, and then intermittently.
2. Multiplication Center
Materials:
Concrete objects that depict a problem (e.g. 3 packs of 24 paper clips) in numbered bags
Numbered Place value mats,
Base ten materials
Description:
Students will choose a bag and solve the problem on the correspondingly numbered place value mat. The teacher can then check solutions before the child leaves the center.
