Multiplying Two Digit by One Digit Numbers with Regrouping

Description: Links are made to the concrete experiences and the contexts used at the concrete level.

(See Build Meaningful Student Connections). Problem solving is emphasized (See Explicit Teacher Modeling)

Purpose: to assist students to build meaningful connections between what they know about problems using concrete objects and using drawings to solve two digit by one digit multiplication problems with regrouping.

* The following description is an example of how you might implement this instructional strategy for Learning Objective 1. A similar process can be used for the other learning objectives in this plan.

Learning Objective 1: Solve two digits by one digit multiplication problems with regrouping using drawings to show the process of repeated addition.

Materials:

Teacher –

Packages of items
Area for visual display,
Place value mat,
Base ten blocks and ten sticks,
Poster of DRAW strategy
Description:

1.) L ink to students’ prior knowledge of multiplying two digit by one digit numbers with regrouping using concrete objects and using the DRAW strategy to solve problems.

For Example:

We have been working on math problems that involve regrouping with multiplication. We have been using counting blocks, ten sticks and place value mats to help us solve these problems. We have been figuring out problems like how many football cards we would have if we had 3 packs of cards with 15 cards in each pack (show items).

2.) I dentify the skill students will learn: Multiply two digits by one digit numbers with regrouping using drawings.

For Example:

Today will we learn how to use the DRAW strategy to solve these problems. We have used the DRAW strategy to help us work problems before. Who can tell me what the D stands for? (Point to poster). What about the R? The A and the W? Right, that is the DRAW strategy. Today instead of using base ten blocks, ten sticks and place value mats (show items), we are going use the DRAW strategy and use lines and circles to solve these multiplication problems. Just like we have been doing, we are going to solve multiplication problems that involve regrouping.

3.) P rovide rationale/meaning for solving two digit by one digit multiplication problems with regrouping.

For Example:

It’s not always convenient for us to carry around cubes, sticks, and our place value mats. By learning to use the DRAW strategy, we can solve multiplication problems with regrouping more quickly.

Purpose: to provide students with a clear teacher model of how to solve two digits by one digit multiplication problems with regrouping using drawings.

Learning Objective 1: Solve two digits by one digit multiplication problems with regrouping using drawings to show the process of repeated addition.

Materials:

Teacher –

Place value mat, blocks, ten sticks,
Visual display board,
Three different colors of markers,
Two sentence strips: “number of groups”, “number of items in each group”
Poster with mnemonics of DRAW strategy,
Group of cookies in bags
Description:

A. Break down the skill of solving two digits by one digit multiplication problems with regrouping using drawings to show the process of repeated addition.

1). Introduce meaningful context.

2.) Introduce/review DRAW strategy steps

3.) Use the DRAW strategy to Discover the sign.

4). Use the DRAW strategy and Read the problem:

5). Use the DRAW strategy and Answer:

Draw a place value mat.
Draw number of groups.
Draw number of items/group.
Count one lines and trade groups of 10.

6). Use the DRAW strategy and Write the answer:

Count the ones lines and write the answer.
Count the ten lines and write the answer.

7). Repeat the multiplication problem.

8.) Repeat at least 2 times using different number combinations.

9.) PRIOR to moving to Learning Objective 2, continue following the teaching plan for Objective 1 by next SCAFFOLDING student learning, moving then to STUDENT PRACTICE STRATEGIES, EVALUATION, and MAINTENANCE.

Learning Objective 2: Solve two digits by one digit numbers with regrouping using drawings to show how numbers are regrouped.

* PRIOR to teaching this objective, the student should have successfully demonstrated independent mastery of the preceding objective

Materials:

Teacher-

Visual display board,
Three different colors of markers,
Two sentence strips: “number of groups”, “number of items in each group”
Posters with mnemonics of DRAW and FIND strategy,
Groups of balloons in bags
Description:

A. Break down the skill of multiplying two digits by one digit numbers with regrouping using drawings to show how numbers are regrouped.

1.) Use the DRAW strategy to Discover the sign.

2.) Use the DRAW strategy and Read the problem:

Use the FIND strategy to find factors’ place values

3.) Use the DRAW strategy and Answer :

Draw a place value mat.
Draw answer for multiplying the ones
Count one lines and trade groups of 10.
Draw answer for multiplying the tens

4.) Use the DRAW strategy and Write the answer:

Count ones lines and write the answer
Count ten lines and write the answer
5.) Repeat the multiplication problem.

Learning Objective 3: Solve two digits by one digit multiplication problems with regrouping by using drawings to illustrate the algorithmic process.

* PRIOR to teaching this objective, the student should have successfully demonstrated independent mastery of the preceding objective.

Materials:

Teacher-

A. Break down the skill of multiplying two digit by one digit numbers with regrouping using drawings to illustrate the algorithmic process.

1.) Use the DRAW strategy to Discover the sign.

2.) Use the DRAW strategy and Read the problem:

Use the FIND strategy to identify factors’ place value
3.) Use the DRAW strategy and Answer :

Draw a place value mat.
Draw answer for multiplying the ones
Draw answer for multiplying ten

4.) Use the DRAW strategy and Write the answer:

Count ones lines and write the answer.
Count ten lines and write the answer.
5.) Repeat the multiplication problem.

Purpose: to provide students an opportunity to build their initial understanding of how to solve two digit by one digit multiplication problems with regrouping using drawings.

Materials:

* Dependent on the skill (See materials listed for the specific skill under Explicit Teacher Modeling).

Description:

Scaffolding at the representational/drawing level of instruction should occur using the same process as scaffolding instruction at the concrete level of instruction (See the description of Scaffolding Instruction for “using concrete objects to solve two digit by one digit multiplication problems with regrouping” in the Concrete Level Instructional Plan). The steps used during Explicit Teacher Modeling should be used as structure for scaffolding your instruction.

1. Scaffold instruction using a high level of teacher direction/support (*Dependent on the needs of your students, you may want to continue to associate concrete materials with drawings at this level as described under Explicit Teacher Modeling.) *Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.

2. Scaffold instruction using a medium level of teacher direction/support (*If you associated concrete materials with drawings while scaffolding using a high level of teacher direction/support, then do not include concrete materials during this phase of scaffolding). *Move to the next phase of scaffolding only when students demonstrate understanding and ability to respond accurately to your prompts.

3. Scaffold instruction using a low level of teacher direction/support (*Students should actually draw as you prompt during this phase of Scaffolding Instruction.). *Move students to independent practice of the skill only after they demonstrate the ability to perform the skill with limited prompting from you.

Purpose: To provide students with multiple practice opportunities to multiply two digit by one digit numbers with regrouping using the drawings to illustrate the algorithmic process.

Learning Objective 3: Multiply two digits by one digit numbers with regrouping using the drawings to illustrate the algorithmic process

Structured Peer Tutoring

Materials:

Teacher –

Sample of problem sheets
Prompt sheet and response sheet to use when introducing and modeling activity.
Students -

Sets of problem sheets. –Each sheet will be divided vertically. On one side will be a multiplication problem. On the other side will be three drawn solutions, one of which is the correct solution.
Prompt sheets,
Response sheets,
Pencils
Description:

Activity:

Students will work in pairs. Each student will have a turn being a coach and being a player. The coach will have 10 problem sheets and a prompt sheet. The prompt sheet will illustrate the steps to solving the problem (see break down of steps in Explicit Teacher Modeling). The player will have a piece of paper with 10 boxes. Each box will be numbered 1-10 and will have 2 blank lines in it. The coach will show the player one of the problem sheets. The player will need to choose the solution to the problem. The coach will turn the sheet over, check the player’s answer, and put a 5 on the first blank line in the box if the player gets the answer right the first time. If the player does not have the correct response, the coach will review the sequence of steps with the player. The player will have a second attempt to choose the correct solution, with the coach providing prompts. After the player correctly chooses the solution, the coach puts a 2 on the second blank line in the box. After the player has completed a set of 10 problems, the coach and player total the player’s points and then switch roles using a different set of problem sheets.

Structured Peer Tutoring Steps:

1.) Select pair groups and assign each pair a place to practice (try to match students of varying achievement levels if possible).

2.) Review directions for completing structured peer tutoring activity and relevant classroom rules. Practice specific peer tutoring procedures as needed (see step #4).

3.) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model both what the coach does (e.g. reads the questions/prompts on the learning sheet; check answers using number card; provide corrective feedback; record points) and how the player responds (e.g. choosing the solution, using the mnemonic). Prior to starting this activity, the teacher will introduce the activity and model how :

a. A player selects a problem sheet, and reviews the strategy.

b. A coach watches the player and provides feedback and positive reinforcement.

c. A coach uses the prompt sheet to assist the player to rethink his/her answer.

d. A player accepts feedback and reinforcement from the coach.

e. A player rethinks an answer that is not correct.

f. A coach re-checks the answer and provides feedback and positive reinforcement.

g. One or both partners can signal the teacher if a question arises.

h. Partners will switch roles once the player has completed one set of 10 problems.

4.) Divide the practice period into two equal segments of time. One student in each pair will be the player and the other student will be the coach.

5.) Provide time for student questions.

6.) Signal students to begin.

7.) Signal students when it is time to switch roles.

8.) Monitor students as they work in pairs. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate tutoring behaviors. Also provide corrective feedback and modeling as needed.

a. Circulate around the room to ensure that all pairs are actively engaged.

b. Set individual goals for students and monitor progress towards those goals.

c. Provide corrective feedback and positive reinforcement to coaches and players.

d. Collect response sheets to track student progress.

e. Provide whole-group review with one or more problems after all pairs have finished.

Purpose: to provide students multiple opportunities to solve two digit by one digit multiplication problems with regrouping by using drawings to illustrate the algorithmic process.

Learning Objective 3: Solve two digits by one digit multiplication problems with regrouping by using drawings to illustrate the algorithmic process.

Self-Correcting Materials

Materials:

Teacher –

Sets of note-cards or problem sheets with multiplication problem on front and answer drawn on back. Note cards should be numbered (e.g. 1-10).
Sets of learning sheets with boxes corresponding to the numbers on note cards. Each learning sheet will have a place for students to record their correct and incorrect responses - “C” (Correct) and “H” (Help).
Students -

A set of note cards
A set of learning sheets
Pencil for drawing/writing
Description:

Activity:

Each student will have a set of note cards and learning sheets. Students pick a note card and solve the problem by drawing the answer in the corresponding box on their learning sheets. The students check their answers by turning the card over where the correct drawing appears along with the answer to the written problem. Students mark their answer as correct or incorrect.

Self-Correcting Materials Steps:

1.) Introduce self-correction material.

2.) Distribute materials.

3.) Provide directions for self-correcting material, what you will do, what students will do, and reinforce any behavioral expectations for the activity.

4.) Provide time for students to ask questions.

5.) Model performing skill (e.g. choosing card, finding appropriate box on learning sheet, drawing answer).

6.) Model how students can check their responses.

7.) Have students practice one time. Provide specific feedback/answer any additional questions as needed.

8.) Monitor students as they work.

9.) Provide ample amounts of positive reinforcement.

10.) Provide specific corrective feedback. Remodel skill as needed,

11.) Encourage students to review their individual learning sheets, write the total number of correct responses next the “C” (Correct) and do the same for the “H” (Help).

Purpose: to provide the teacher 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
Students:
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, the expressive level, or both.

2.) Choose appropriate criteria to indicate mastery.

3.) Provide appropriate prompts in an appropriate format (receptive/recognition or expressive) so students can respond:

4.) Based on the skill, your students’ learning characteristics, and your preferences, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with prompts), or oral in nature with visual cues (e.g. teacher shows several drawings/choices on overhead then prompts students to say which drawing shows the correct solution for the problem), or a combination of both (e.g. teacher shows problem and then prompts students to circle which of several drawings shows the correction solution).

5.) Provide students with the materials to complete each task.

6.) Provide directions on how to complete each task.

7.) Conduct evaluation.

8.) Count corrects and incorrects (you and/or students can do this dependent on type of curriculum slice/probe used).

9.) You and/or the students will plot their responses on a suitable chart. A goal line that represents proficiency should be visible on each student’s chart. For representational level of understanding this should be 100%. for 8 –10 trials.

10.) Talk with children about their progress as it relates to.the goal line and their previous performance. Prompt them to self evaluate (Did you use the DRAW/FIND strategy?)

11.) Evaluate whether student(s) is ready to move to the next level of understanding or has mastered the skill by demonstrating 100% accuracy for 8-10 trials over 2-3 days.

12.) Determine whether you need to alter or modify your instruction based on student performance.

Flexible Math Interview

Purpose: to provide the teacher with additional diagnostic information in order to check student understanding, and plan and/or modify instruction accordingly.

Materials:

Teacher –

Appropriate multiplication problems
Students -

Paper, pencils
Description:

With individual students or in small groups, the teacher will have students draw solutions to given multiplication problems. The teacher will ask students to explain how their drawings show the solution to the problem. The teacher should note errors 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 confers with students regarding specific errors or misconceptions afterwards.

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:

Multiplication problems
Paper/pencil
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. Transition Filler/Rapid Fire Verbal Review

Materials:

* Dependent on routine

Description:

While lining up or during other transitional times, the teacher will ask students to say/show the steps of the DRAW strategy (e.g. “Okay, while we are waiting to be called to the assembly, let’s review what DRAW stands for (cover poster/display with mnemonic Doug, what does the D stand for? Right. Good. Jason, what about the R? Tammy, what about the A, and Felicia the W?) Continue to ask students steps, reinforcing accurate and automatic responding.