Mathematical strategies Robin Linton

Self-Monitoring Strategies in MATH Provide students with a guide that prompts them to remember how to complete a task. Checklist 1. Carefully analyze the skill to be taught and identify the critical steps to be performed. 2. Write down steps at a level that can be understood by the student 3. Organize the written statements in sequential order. 4. Place the complete checklist next to each problem as it is done. Explain the checklist and give a concrete example of how to use self-monitoring component

Modifications for Use with Addition 4 Critical Steps to solving multi-digit addition problems: 1. Start in the 1s column 2. Add together the numerals in each column 3. Determine whether or not regrouping is necessary 4. Check to see whether or not the correct numeral has been carried to the next column when regrouping is necessary. The word SASH can be used as mnemonic strategy to help students remember the steps: (Start in the 1s column; Add the numerals together; Should I carry a numeral? And Have I carried the correct numeral?)

SUBTRACTION ILLUSTRATION 4 critical steps solving multi-digit subtraction problems 1. Starting in the 1st column 2. Determine which numeral in each column is bigger 3. Regrouping if the bottom numeral is bigger 4. Check basic facts The mnemonic strategy “4Bs” helps students remember the 4 steps: Begin, Bigger, Borrow and Basic Facts The student begins the first problem by looking at the first step at the list of directions. Starting with Begin-the student then places a check mark on the line by Begin.

Modifications for use with multiplications There are 4 critical steps in solving multi-digit multiplication problems. 1. Multiply the 1s column. 2. Carry any 10s over to the 10s column 3. Multiply the bottom 1s digit with the top 10s digit 4. Add any number that was carried in step 2 to the product of step 3 The word MAMA can be used as a mnemonic strategy to help students remember the steps: (Multiply the 1s column; Across to the 10s; Multiply the bottom 1s digit with the top 10s digit; Add any number that was carried in step 2.

SLOBS & LAMPS These math strategies are designed to help students remember the regrouping process of borrowing and carrying. Slobs are used in subtraction and lamps are used in addition. SMALLER Smaller. Follow steps. LARGER Larger, Leap to subtract. OFF Cross Off the number in the next column BORROW Borrow, by taking one ten and adding to the next column SUBTRACT

ARITHMETIC MIND JOGGER This is how one would follow these steps with the following problem: 72 46 Look at the top number on the right (2) and see if it is smaller or larger than the lower number (6). If it is larger, the student will leap to subtract. If it is small as in the example, the student must follow the steps. The next step is to cross off the number in the next column, which in this problem is the seven. The “B” of SLOBS stands for borrow, which is the next step. Now borrow one ten from that column by reducing the number by one and adding ten to the other number (12). The last step is to subtract the six from the twelve. Repeat the steps if there are more digits to be subtracted.

LAMPS LINE SEND Send the tens to the top of the next column. Lineup the numbers This is particularly important with extensive columns of numbers and with numbers with decimal points. ADD Add the right column of numbers and ask… MORE More than nine? If so, do more steps. PUT Put the ones below the column. SEND Send the tens to the top of the next column.

Video of 4th Grade Math Class Elementary Class: http://www.pd360.com/index.cfm?ContentId=7027 http://www.pd360.com/index.cfm?ContentId=703 1 5th Grade Calls: http://www.pd360.com/index.cfm?ContentId=100 3

Teach students to use visual representations Select visual representations that are appropriate for students and the problems they are solving. Use think-alouds and discussions to teach students how to represent problems visually. Show student how to convert the visually represented information into mathematical notation.

FRACTIONS

KHAN ACADEMY-VIDEOS Multiplication http://www.khanacademy.org/math/arithmetic/m ultiplication-division/multiplication_fun/v/basic- multiplication Linear Equations http://www.khanacademy.org/math/cc-sixth-grade- math/cc-6th-expressions-and-variables/cc-6th- beginner-equations/v/simple-equations

Expose students to multiple problem-solving strategies Provide instruction in multiple strategies. Provide opportunities for students to compare multiple strategies in worked examples. Ask students to generate and share multiple strategies for solving problems.

Assist students in monitoring and reflecting on the problem-solving process Provide students with a list of prompts to help them monitor and reflect during the problem- solving process. Model how to monitor and reflect on the problem- solving process. Use student thinking about a problem to develop student’s ability to monitor and reflect.

Writing in Mathematics Video http://www.pd360.com/index.cfm?ContentId=320

References Council for Exceptional Children What Works Guidance Document: Improving Mathematical Problem Solving in Grades 4 through 8. PD 360 Khan Academy