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Math Interventions

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Least Intensive Interventions
Moderate/Intensive Interventions


Least Intensive Interventions

Number Search

Materials: A place from which to observe, paper and a pencil

Intervention: Create a chart that lists the numbers from 1-50. Write down each number as family members locate that number on a car, a sign, a building, etc. Write down words that have numbers in them, such as "one-stop shopping," "two-day service," or "Highway 20." This is a great challenge for family members of all ages, because even young children can learn to recognize numbers.

Courtesy of:
http://www.ed.gov/pubs/parents/Math/OnTheGo.html

“Cover-Copy-Compare”

Category: Math Skills

Grade: May use with any age group. Activity is dependent on current curriculum

Materials: Teacher prepared worksheets with computation problems with answers on the left side of the sheet. Completed computation problems appear on the right side of the page, unsolved.

Intervention: When first introducing Cover-Copy-Compare worksheets to the student, the teacher gives the student an index card. The student is then directed to look at each correct computation on the left side of the page. Then the student is instructed to cover the correct model on the left side of the page with an index card and to copy the problem and compute the correct answer in the space on the right side of the sheet. The student then uncovers the correct answer on the left and checks his or her own work. If the use of an index card proves distracting you may simply fold the worksheet in half length-wise so that the answers appear on one side of the folded worksheet and the answer blanks appear on the other side. An advantage of this intervention is the ability of the child to work independently and correct his or her work. It’s important that the student does not just copy the problems. He or she must study the completed computation, then work to solve the problem autonomously. If the child needs to be supervised, the use of a peer may tutor may be helpful.

Courtesy of:
http://www.interventioncentral.org/htmdocs/interventions/ccc.shtml

More or Less

Materials: Coin, 2 decks of cards, Scratch paper to keep score

Age or Grade: Kindergarten-Grade 2

Intervention: This game encourages number sense and helps children learn about the relationships of numbers and about adding and subtracting. By counting the shapes on the cards and looking at the printed numbers on the card, they can learn to relate the number of objects to the numeral. First flip a coin to tell if the winner of this game will be the person with "more" (a greater value card) or "less" (a smaller value card). Remove all face cards and divide the remaining cards in the stack between the two players. Place the cards face down. Each player turns over one card and compares: Is mine more or less? How many more? How many less?

Courtesy of:
http://www.ed.gov/pubs/parents/Math/Home.html

Money Match

Materials: a die to roll, 10 of each coin (penny, nickel, dime), 6 quarters

Intervention: This game helps children count change. Lots of repetition will make it even more effective. For young players (5-and 6-year-olds), use only 2 different coins (pennies and nickels or nickels and dimes). Older children can use all coins. Explain that the object of the game is to be the first player to earn a set amount (10 or 20 cents is a good amount). The first player rolls the die and gets the number of pennies shown on the die. Players take turns rolling the die to collect additional coins. As each player accumulates 5 pennies or more, the 5 pennies are traded for a nickel. The first player to reach the set amount wins. Add the quarter to the game when the children are ready. Counting money, which involves counting by 1's , 5's, 10's and 25's is a challenging skill and usually does not come easily to children until about the third grade.

Courtesy of:
http://www.ed.gov/pubs/parents/Math/Home.html

Math Word Problem Strategies

Intervention:

  1. Make certain the student's inability to read is not the cause of his/her difficulty.
  2. Teach the student to look for "key words" that will indicate the math operation. Make or provide a list of these key words.
  3. Before introducing complete word problems, present the student with word phrases to be translated into numbers (six less than ten equals 10-6).
  4. Provide the student with a checklist to follow in solving math story problems.
  5. Make the situation interesting to the student. Have the student make up story problems

Reference: Mc Carney, The Teacher's Resource Guide, Hawthorne

Difficulty With Word Problems

Age or Grade: Grade 6 – Grade 8

  • Intervention #1 – The teacher may ask the student to identify the primary question that must be answered to solve a given word problem. The teacher should continue this activity using more difficult word problems containing two or more questions, making sure the student understands the questions are often implied rather than directly asked.
  • Intervention #2 – The teacher can have the student make up word problems. Direct the student to write problems involving specific operations. Other students in the classroom should be required to solve these problems. The student can also provide answers to his/her own problems.
  • Intervention #3 – The teacher can speak with the student to explain: (a) what the student is doing wrong (e.g., using the wrong operation, failing to read the problem carefully, etc.) and (b) what the student should be doing (e.g., using the appropriate operation, reading the problem carefully, etc.)

Reference: McCarney, S.B., Cummins Wunderlich, K., Bauer,A, (1994). The Teacher's Resource Guide: Colimbia, MO.

Collaborative Problem Solving

Collaborative problem solving can take the form of long-term projects or shorter activities that can be completed in a single class period or less. Students enjoy puzzles in which each person in a group of four is given a different clue and the clues must be combined to reach the solution. Both number sense and mental math skills are developed when students are challenged to find a number which is even, is a multiple of three, has an integral square root and has two digits.

Reference: Cole, R.W, (1995). Educating Everybody's Children: Diverse Teaching Strategies for Diverse Learners. Alexandria, Va. ASCD

Small Group

Small Class Size (13-17 Students) – There are lasting benefits in mathematics achievement at grade 9 when students are in small class sizes in the early grades.

Courtesy of:
The University of Chicago School “Everyday Mathematics”http://everydaymath.uchicago.edu/

Addition Top-It

Materials: A set of number cards with four cards each of the numbers 0-10, a penny (optional)

Number of Players: 2 or 3

Directions: A player shuffles the cards and places the deck number-side down on the playing surface. Each player turns over two cards and calls out their sum. The player with the highest sum wins the round and takes all the cards.
In the case of a tie, each player turns over two more cards and calls out their sum. The player with the highest sum then takes all the cards from both plays.
Play ends when not enough cards are left for each player to have another turn. The player with the most cards wins.

Option: Children toss a penny to determine whether the player with the most or the fewest cards wins.

Game Variations

  1. Use a set of double-nine dominoes instead of a set of number cards to generate addition problems. Place the dominoes facedown on the playing surface. Each player turns over a domino and calls out the sum of the dots on the two halves. The winner of a round takes all the dominoes then in play.
  2. To practice addition with three addends, use three cards.

Courtesy of:
The University of Chicago School “Everyday Mathematics”http://everydaymath.uchicago.edu/

Name that Number

Materials: 4 cards each of numbers 0-10 and 1 card each of numbers 11-20

Number of Players: 3 or 4

Directions: A player shuffles the deck and places five cards face-up on the playing surface. This player leaves the rest of the deck facedown and then turns over and lays down the top card from the deck. The number on this card is the number to be named. In turn, players try to (re)name the number on the set-apart top card by adding or subtracting the numbers on two of the five face-up cards. A successful player takes both the two face-up cards and the number-named top card. A successful player also replaces those three cards by drawing from the top of the facedown deck. Unsuccessful players lose their turns. But they turn over and lay down the top card from the facedown deck, and the number on this card becomes the new number to be named. Play continues until all facedown cards have been turned over. The player who has taken the most cards at the end wins.

Example:

Mae's Turn:
Mae's Cards
The number to be named is 6. It may be named with 4+2, 8-2 or 10-4. Mae selects 4+2. She takes the 4, 2 and 6 cards. She replaces the 4 and 2 cards with the top two cards from the facedown deck and then turns over and lays down the next card to replace the 6.

Mike's Turn:
Mike's Cards
The new number to be named is 16. Mike can't find two cards with which to name 16, so he loses his turn. He also turns over the next card from the facedown deck and places it on top of 16, and the number on this card becomes the new number to be named.

Play continues as before.

Game Variations:

  • If children are finding the game difficult, increase the number of face-up cards.
  • Use any combinations of two or more numbers and all operations. For example, Mike could have named 16 as follows:
    • 10+7-1
    • 10+12-7+1
    • 8+12-10+7-1
  • Children can experiment by using different numbers of face-up cards.

Courtesy of:
The University of Chicago School “Everyday Mathematics”http://everydaymath.uchicago.edu/

Two-Fisted Pennies Game

Materials: 10 pennies for each player

Number of Players: 2 or more

Directions: Players count out 10 pennies, and then split them between their two hands. (Help children identify their left and right hands.) Call on several children to share their amounts. For example: "My left hand has 1 and my right hand has 9; left hand 3 and right hand 7; left hand 4 and right hand 6; left hand 5 and right hand 5." Record the various splits for any given number on the chalkboard. Partners continue to play using different total numbers of pennies – for example, 9, 12, 20.

Option: Partners take turns grabbing one part of a pile of 20 pennies. The other partner takes the remainder of the pile. Both players count their pennies, secretly. The partner making the grab uses the count to say how many pennies must be in the partner's hand. ("I have 12, so you must have 8." The eventual result is many addition names for 20. Change the number of pennies in the pile to practice addition names for other numbers.

Courtesy of:
The University of Chicago School “Everyday Mathematics” http://everydaymath.uchicago.edu/

Beat the Calculator

Materials: a calculator; a penny or a random-number generator (optional); 1 Fact Power Table (optional)

Number of Players: 3

Directions: One player is the "Caller," a second player is the "Calculator," and the third is the"Brain." The "Caller" selects a fact problem by dropping a penny on Game Master 7 or by using a random-number generator to create an addition-fact problem. The "Calculator" then solves the problem with a calculator while the "Brain" solves it without a calculator. The "Caller" decides who got the answer first.

Players trade roles every 10 turns or so.

Taken from K-3 Everyday Mathematics Teacher's Reference Manual.

Courtesy of:
The University of Chicago School “Everyday Mathematics” http://everydaymath.uchicago.edu/

General Math Strategies

Strategies for factual learning:
1. Count-on, count-by, touch-math, etc.
2. Use for students when the data shows it’s working

Strategies for complex problems:
1. “Daddy, Mother, Sister, Brother” – Steps for long division. Divide, Multiple, Subtract, Bring down

Strategies for solving word-problems:
1. Provide an advance organizer (tell students what they will learn and why).
2. Explicitly model strategic behavior using think-aloud approach.
3. Give guided practice.
4. Provide feedback during independent practice.

Courtesy of:
Using Progress Monitoring as Data-Based Decision-Making: Materials for Trainers, Presentation for ESU #1, Spring 2006, Dr. Erica Lembke, University of Missouri

Number Sense

The student will understand numbers, ways of representing numbers, relationships among numbers and number systems. Start teaching with categories: counting, reading and writing number symbols and words, relationships among whole numbers, place value, estimation.

  • Counting strategy: Rote counting intervention: Each day, practice counting up to the highest number the student reached on the previous day. If mastered, add two more numbers. If not, practice numbers from the previous day. Practice counting with 1, but also beginning and ending with other numbers (i.e., begin at 8 and stop at 17). This leads to counting strategies that will be helpful in addition. Also, have the student count backwards.
  • Rational counting: Counting items (concrete or pictorial) in a picture (need 1-1 correspondence). Given two groups of objects, student will count how many altogether.
  • Ordinal counting: Identify ordinal position of objects in a line (first, second, third, etc.)
  • Skip counting: Count objects/pictures by 2’s, 5’s, and 10’s to 100. Skip count by 2’s, 5’s, and 10’s orally. Recognize and extend patterns by filling in missing numbers.
  • Number symbols: Say names when shown number symbols. Write numbers given the oral number name.
  • Number words: Read number words. Write number words that are presented orally.
  • Writing numbers sequences: Write the missing numerals that fill in the sequence.
  • Symbol quantity match: Match number symbols to correct quantities of pictorial or concrete objects. Count out objects that match a given number symbol.
  • One-to-one correspondence between groups: Match objects from one group to objects in another using 1-1 correspondence.
  • Quality comparison: Are groups of objects equal in number? Which group has more or fewer? Arranging groups of objects in order from smallest to largest. Use symbols <, >, =. Identify number that is greater than, less than or equal to.
  • Place value: “Trade” ones to make tens. Identify the numbers from concrete or pictorial representations of base 10 blocks. Represent numbers with base 10 blocks.
  • Column alignment: Align 2 numerals with differing numbers of digits vertically.
  • Expanded notation: Rewrite multidigit numbers as addition problems.
  • Place value recognition: Identify the value of each place in a mutlidigit number.
  • Base ten identification: Given a number, identify 1 or 10 more or less.
  • Estimation: Estimate how many concrete or pictorial objects are in a group.

Courtesy of:
Using Curriculum-Based Measurement (CBM) within a Response to Intervention System: Data Utilization, Presentation for ESU #1, January 2007, Dr. Erica Lembke, University of Missouri.


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Moderate/Intensive Interventions

Peer-Mediated Instruction

Suggestions for Implementing Successful Peer-Mediated Instructional Arrangements:

  1. Establish rules and guidelines to help students function as a group and work cooperatively. (Johnson & Johnson, 1990)
  2. Form heterogeneous groups based on such factors as gender, race, ethnicity, linguistic ability, academic and social level and ability to work together. (Dishon & O'Leary, 1991; Edwards & Stout, 1990)
  3. Arrange the physical design of the classroom to facilitate peer-mediated instruction. (Johnson & Johnson, 1986)
  4. Help students learn to work cooperatively. (Johnson & Johnson, 1990; Whittaker, 1991)
  5. Deal with problems that typically occur with peer-mediated instructional arrangements, such as increased noise levels, complaints about partners and cheating. (Maheady, Harper, & Mallette, 1991)

Courtesy of:
www.deafed.department.tcnj.edu/math/peermediated.html

PALS (Peer Assisted Learning Strategies)

Peer Assisted Learning Strategies (PALS) is a class-wide peer-tutoring program providing supplemental practice and instruction on key reading skills. K-PALS focuses on phonemic awareness, alphabetic principle and sight word reading. First Grade PALS focuses on alphabetic principle, fluency and sight word reading. Second-Eighth Grade PALS focuses on fluency and accuracy in connected text and reading comprehension strategies of summarization, main idea and predication. High School PALS focuses on Fluency and comprehension skills within the context of a career, job oriented structure. Lessons are provided to train students to be “readers and coaches.” Students are taught correction procedures and instructional cues. K=8 PALS can be used in general or special educational classrooms. High School PALS has only been validated in special education and remedial settings.

Program: PALS (Peer Assisted Learning Strategies)
Publisher/Source: Vanderbilt University
Educational level: K, 1, 2-6, 7-12
Authors: Lynn and Doug Fuchs


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Questions? Comments? Please email Scott or Tracey.