Two Digit by One Digit Numbers with Regrouping: Abstract Level
Teaching Plans on this topic: Concrete, Representational
PHASE 1: Initial Acquisition of Skill
Teach Skill with Authentic Context
Description: Links are made to the contexts used at the representational level. (See Build Meaningful Student Connections). Problem solving is emphasized (See Explicit Teacher Modeling) Meaningful contexts will continue to be used in the form of story situations that have relevance for 9-11 year old students. It is important always to provide story situations that have relevance to your students given their age, cultural backgrounds, and interests.
Build Meaningful Student Connections
Purpose: to assist students to build meaningful connections between what they know about using drawings and solving two digit by one digit multiplication problems with regrouping by using the algorithmic process.
- Popsicle box
- Package of napkins
- White board or other visual displayMarkers/chalk
- Poster with mnemonics for DRAW and FIND strategies
- Place value mat, base ten materials
- Example of solving multiplication problem with drawing
1) L ink to students’ prior knowledge of multiplying two digits by one digit numbers with regrouping using drawings.
Can everyone see what I have up here? I have a box of Popsicles. Today we are going to plan a multiplication celebration because you all have been working so hard learning multiplication. You are going to help me make sure that I have planned it all out and that I have enough food for everyone. We have used base ten materials (show example) and drawings (show example) to solve multiplication problems. Now we are going to just use numbers.
2) I dentify the skill students will learn: Solve two digits by one digit multiplication problems with regrouping by using the algorithmic process.
We have been solving multiplication problems by drawing. Today we are going to learn how to do multiplication problems by just using numbers. We are going to figure out if I have bought enough Popsicles and napkins for our celebration. We are going to use our multiplying skills to figure this out. I want to make sure that each of you has one Popsicle. There are 35 students in the fourth grade plus myself so we have 36. Then I want to make sure that we have enough to give one to each of our principals and our secretaries. That makes 40 people. Each box has 14 popsicles in it. I have bought 3 boxes. I am going to have you help me to see if I bought enough boxes.
3) P rovide rationale/meaning for learning how to multiply two digit by one digit numbers with regrouping without drawing.
It’s good that we can draw to help us find our answers when we multiply, but sometimes we may not want to draw all of those lines, particularly when the numbers get bigger. We can do harder problems quicker if we learn to multiply without using drawings.
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Provide Explicit Teacher Modeling
Purpose: to provide students a clear teacher model of how to solve two digits by one digit multiplication problems with regrouping by using the algorithmic process.
Learning Objective 1: Solve two digits by one digit multiplication problems with regrouping by using the algorithmic process.
- Visual display board
- Colored markers or chalk
- Sentence strips with “number of groups” and “number of items in each group”
- Poster/display of mnemonics for DRAW and FIND strategy
A. Break down the skill of solving two digits by one digit multiplication problems with regrouping by using the algorithmic process.
1) Use the DRAW strategy to Discover the sign
2) Use the DRAW strategy to Read the problem
Use the FIND strategy to identify factors’ place values
3) Use the DRAW strategy and Answer
4) Use the DRAW strategy and Write the answer
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Purpose: Scaffolding at the abstract 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 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 with drawings while scaffolding using a high level of teacher direction/support, then do not include them 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 solve problems 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.
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