DESCRIPTION: The student plays a number-based board game to build skills related to 'number sense', including number identification, counting, estimation skills, and ability to visualize and access specific number values using an internal number-line (Siegler, 2009).
GROUP SIZE: 1-2 students
TIME: 12-15 minutes per session
MATERIALS:
Great Number Line Race! Form (attached)
Spinner divided into two equal regions marked "1" and "2" respectively. (NOTE: If a spinner is not available, the interventionist can purchase a small blank wooden block from a crafts store and mark three of the sides of the block with the number "1" and three sides with the number "2".)
INTERVENTION STEPS: A counting-board game session lasts 12 to 15 minutes, with each game within the session lasting 2-4 minutes. Here are the steps:
Introduce the Rules of the Game. If the student is unfamiliar with the counting board game, the interventionist trains the student to play it.
-The student is told that he or she will attempt to beat another player (either another student or the interventionist). The student is then given a penny or other small object to serve as a game piece. The student is told that players takes turns spinning the spinner (or, alternatively, tossing the block) to learn how many spaces they can move on the Great Number Line Race! board. Each player then advances the game piece, moving it forward through the numbered boxes of the game-board to match the number "1" or "2" selected in the spin or block toss.
-When advancing the game piece, the player must call out the number of each numbered box as he or she passes over it. For example, if the player has a game piece on box 7 and spins a "2", that player advances the game piece two spaces, while calling out "8" and "9" (the names of the numbered boxes that the game piece moves across during that turn).
-The player who reaches the "10" box first is the winner.
Record Game Outcomes. At the conclusion of each game, the interventionist records the winner using the form found on the Great Number Line Race! form. The session continues with additional games being played for a total of 12-15 minutes.
Continue the Intervention Up to an Hour of Cumulative Play. The counting-board game continues until the student has accrued a total of at least one hour of play across multiple days. (The amount of cumulative play can be calculated by adding up the daily time spent in the game as recorded on the Great Number Line Race! form.)
DESCRIPTION: The student is taught explicit number counting strategies for basic addition and subtraction. Those skills are then practiced with a tutor (adapted from Fuchs et al., 2009).
MATERIALS:
Number-line (attached)
Number combination (math fact) flash cards for basic addition and subtraction
Strategic Number Counting Instruction Score Sheet (attached)
PREPARATION: The tutor trains the student to use these two counting strategies for addition and subtraction:
ADDITION: The student is given a copy of the appropriate number-line (1-10 or 1-20—see attached). When presented with a two-addend addition problem, the student is taught to start with the larger of the two addends and to 'count up' by the amount of the smaller addend to arrive at the answer to the problem.
SUBTRACTION: The student is given a copy of the appropriate number-line (1-10 or 1-20—see attached).. The student is taught to refer to the first number appearing in the subtraction problem (the minuend) as 'the number you start with' and to refer to the number appearing after the minus (subtrahend) as 'the minus number'. The student is directed to start at the minus number on the number-line and to count up to the starting number while keeping a running tally of numbers counted up on his or her fingers. The final tally of digits separating the minus number and starting number is the answer to the subtraction problem.
INTERVENTION STEPS: For each tutoring session, the tutor follows these steps:
Create Flashcards. The tutor creates addition and/or subtraction flashcards of problems that the student is to practice. Each flashcard displays the numerals and operation sign that make up the problem but leaves the answer blank.
Review Count-Up Strategies. At the opening of the session, the tutor asks the student to name the two methods for answering a math fact. The correct student response is 'Know it or count up.' The tutor next has the student describe how to count up an addition problem and how to count up a subtraction problem. Then the tutor gives the student two sample addition problems and two subtraction problems and directs the student to solve each, using the appropriate count-up strategy.
Complete Flashcard Warm-Up. The tutor reviews addition/subtraction flashcards with the student for three minutes. Before beginning, the tutor reminds the student that, when shown a flashcard, the student should try to recall the answer from memory—but that if the student does not know the answer, he or she should use the appropriate count-up strategy. The tutor then reviews the flashcards with the student. Whenever the student makes an error, the tutor directs the student to use the correct count-up strategy to solve. NOTE: If the student cycles through all cards in the stack before the three-minute period has elapsed, the tutor shuffles the cards and begins again.
At the end of the three minutes, the tutor counts up the number of cards reviewed and records the number of cards that the student (a) identified from memory, (b) solved using the count-up strategy, and (c) was not able to correctly answer. These totals are recorded on the Strategic Number Counting Instruction Score Sheet.
Repeat Flashcard Review. The tutor shuffles the math-fact flashcards, encourages the student to try to beat his or her previous score, and again reviews the flashcards with the student for three minutes. As before, whenever the student makes an error, the tutor directs the student to use the appropriate count-up strategy. Also, if the student completes all cards in the stack with time remaining, the tutor shuffles the stack and continues presenting cards until the time is elapsed.
At the end of the three minutes, the tutor again counts up the number of cards reviewed and records the number of cards that the student (a) identified from memory, (b) solved using the count-up strategy, and (c) was not able to correctly answer. These totals are again recorded on the Strategic Number Counting Instruction Score Sheet.
Provide Performance Feedback. The tutor gives the student feedback about whether (and by how much) the student's performance on the second flashcard trial exceeded the first. The tutor also provides praise if the student beat the previous score or encouragement if the student failed to beat the previous score.
Common Core Standards: Varied
Setting: Whole Class
Focus Area: Acquisition, Fluency and Generalization
Overview: Math Wise is a whole-class intervention for second-grade students. With Math Wise, students participate in lessons focused on addition and subtraction of single- and double-digit numbers.
Common Core Standards: Operations and Algebraic Thinking (K-5), Numbers and Operations in Base Ten (K-5) and Numbers and Operations – Fractions (3-5)
Setting: Whole Class, Small Group or Individual
Focus Area (Acquisition, Fluency and Generalization)
Overview: A schema is a way to organize or pattern information within a structured framework of known and unknown information. Within word-problem work, the learner identifies the type of problem (i.e., schema), which lends itself to solving the problem using a given organizational pattern. The main focus of Schema-Based Instruction or Schema-Broadening Instruction (SBI) is to teach word-problem solving using identification of a problem schema, representation using diagrams or equations to represent the schema, and solving the word problem. Scaffolding of student learning is provided throughout.
Common Core Standards: All
Setting: Whole Class, Small Group or Individual
Focus Area: Acquisition, Fluency and Generalization
Overview: With CRA, students work with hands-on materials that represent mathematics problems (concrete), pictorial representations of mathematics problems (representational), and mathematics problems with numbers and symbols (abstract). The teacher explicitly bridges the connection between the concrete, representational, and abstract representations of the mathematics problems.