|
Multiplying Two Digit by One Digit Numbers with Regrouping
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.
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.
Materials:
Teacher –
Popsicle box
Package of napkins
White board or other visual display
Markers/chalk
Poster with mnemonics for DRAW and FIND strategies
Place value mat, base ten materials
Example of solving multiplication problem with drawing
Description:
1.) L ink to students’ prior knowledge of multiplying two digits by one digit numbers with regrouping using drawings.
For Example:
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.
For Example:
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.
For Example:
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.
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.
Materials:
Teacher –
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
Description:
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
Multiply ones
Multiply tens
4.) Use the DRAW strategy and Write the answer
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.
Purpose: To provide students with multiple practice opportunities to recognize correct solutions to problems for multiplying two digit by one digit numbers with regrouping using the algorithmic process
Learning Objective 1: multiply two digit by one digit numbers with regrouping using algorithmic process.
Structured Cooperative Learning/Instructional Games
Materials:
Teacher –
Sample of problem sheet
Students -
Set of problem sheets that each show a multiplication problem and three choices for answers
Description:
Activity:
Children will work in groups of 4 or 5 students. Each group will have a set of problem sheets numbered 1-10. The teacher will choose a problem 1-10. . Each team is to look at the correspondingly numbered problem sheet and decide which of the three given answers is correct. After the teacher rings the bell, one member of each team will come to the board and solve the problem. 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)
b. Time keeper (makes sure that group stays on task)
c. Reporter (reports group’s answer)
d. Encourager(s) (encourages each person)
4.) Distribute materials.
5.) Model one example of skill(s).
a. Look at problem.
b. Look at answer choices
c. Decide which is correct answer,
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 decisions.
c. Attend to classmates showing examples on board.
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 with multiple practice opportunities to solve 0problems for multiplying two digits by one digit numbers with regrouping using the algorithmic process.
Learning Objective 1: Multiply two digit by one digit numbers with regrouping using algorithmic process.
Structured Language Experience
Materials:
Teacher –
Several problems written on board
Visual display of sample journal entry
Students -
Math Journal
Pen/pencil
Description:
Activity:
Teacher will write several problems on board. Students will choose one of the problems, and explain how to solve it in their journal. Teacher will ask selected children or volunteers to share their entries and solve the problem on the board.
Structured Language Experience” Steps:
1.) Review directions for completing structured language experience activity and relevant classroom rules.
2.) Model how to perform the skill(s) within the context of the activity before students begin the activity. Model how to choose one of the problems. Think about how to solve it. Write the steps to solving it. Check your work by actually solving it.
3.) Provide time for student questions.
4.) Signal students to begin.
5.) Monitor students as they work. Provide positive reinforcement for both “trying hard,” responding appropriately, and for students using appropriate behavior. Also provide corrective feedback and modeling as needed.
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 appropriate criteria to indicate mastery.
3.) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.
4.) 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 problems; index cards with problems and choices to match), or oral in nature with visual cues (e.g. show problems a and have students tell you how to solve the problem) or a combination of written curriculum slices/probes and oral prompts with visual cues (e.g. teacher shows problems and answer choices on overhead and then prompts students to write solution to problem).
5.) Distribute to students the curriculum slice/probe/response sheets.
6.) Give directions.
7.) Conduct evaluation.
8.) Count corrects and incorrects/mistakes (you and/or students can do this depending on the type of curriculum slice/probe used – see step #3).
9.) You and/or students plot their scores on a suitable graph/chart.). A goal line should be visible on each students’ graph/chart that represents the proficiency (near 100% accuracy with two or fewer incorrects/mistakes) and a rate (# of corrects per minute) that will allow them to be successful when using that skill to solve real-life problems and when using the skill for higher level mathematics that require use of that skill.
10.) Discuss with children their progress as it relates to the goal line and their previous performance. Prompt them to self-evaluate.
11.) Evaluate whether student(s) has mastered the skill at the abstract level using the following guide:
Abstract Level: demonstrates near 100% accuracy (two or fewer incorrects/mistakes) and a rate (# of corrects per minute) that will allow them to be successful when using that skill to solve real-life problems and when using the skill for higher-level mathematics that require use of that skill.
12.) Determine whether you need to alter or modify your instruction based on student performance.
Error Pattern Analysis
Purpose: to provide you with additional diagnostic information in order to check student understanding and plan and/or modify instruction accordingly.
Materials:
Problem sheets
Description:
Have student complete 5-8 problems. As the student works the problems, encourage him/her to talk about what they are doing. Do not cue student in any way. Record all student responses, verbal and written. Review responses and look for patterns. Also look for examples of “exceptions” to an apparent pattern (accurate exceptions may indicate that the student has partial understanding of the procedure or of a basic concept). Common errors for this skill may be the result of non-understanding of place value, inaccurate procedure/sequence of steps, non-understanding of regrouping, or insufficient mastery of basic multiplication facts.
After you have analyzed the problems for possible error patterns, you may want to interview the student using a Flexible Math Interview to gain further insight before planning how to modify or reteach the lesson.
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:
Written display of problem
Student response cards,
Description:
The teacher will present a problem of the day verbally and by displaying the written problem. Students will solve and turn in their response cards. This should initially be done each day, then 2 times/week, weekly, bi weekly, and then intermittently.
2. Multiplication Bingo
Materials:
Written problems on board
Calculators
Laminated Bingo cards with blank spaces
Bingo counters (beans, chips, paper pieces)
Description:
Students will solve answers to problems on board. They will record their solutions of bingo cards, choosing where to put the answers. The teacher will randomly choose a problem to solve and once solved, any student who has the correction answer covers up a square.
|
