Multiplying Two Digit by One Digit Numbers with Regrouping: Representational Level

More Teaching Plans on this topic: Concrete, Abstract

PHASE 1: Initial Acquisition of Skill

Teach Skill with Authentic Context
Build Meaningful Connections

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.

Provide Explicit Teacher Modeling

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-

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,

Description:

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.

Scaffold Instruction

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.

Videos

Learning Objective 1: view  Clip 1, Clip 2, Clip 3, Clip 4, Clip 5 , Clip 6
Solve two digits by one digit multiplication problems with regrouping using drawings to show the process of repeated addition.

Learning Objective 2: view  Clip 1, Clip 2, Clip 3, Clip 4
Solve two digits by one digit numbers with regrouping using drawings to show how numbers are regrouped.

Learning Objective 3: view  Clip 1, Clip 2
Solve two digits by one digit multiplication problems with regrouping by using drawings to illustrate the algorithmic process.