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Teach Using BIG Ideas


Focusing on "Big Ideas" when teaching math helps facilitate student understanding by concentrating student attention on key concepts and procedures. The linkages and connections between math concepts are made explicit by linking previously learned big ideas to new concepts and problem solving situations. By emphasizing the big ideas in each lesson, teachers can build students' acquisition and use of key conceptual knowledge across lesson content.

What is it?

  • Math Big Ideas are key math concepts that can be continually used to teach a variety of math skills/processes.
  • Provides referential starting points for students when learning new math concepts/skills.
  • Examples include "objects and groups", place-value, area, proportion, (part-whole relationships) estimations, etc.)
  • Math Big Ideas are explicitly described and modeled by the teacher.

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What are the critical elements of this strategy?

  • Key concepts, math big ideas that can be used within and across knowledge strands are identified.
  • Student attention is focused on these key math big ideas.
  • Accompanying skills and procedures are directly and systematically taught, using explicit teaching techniques.
  • Linkages between math Big Idea and target math skill are explicitly demonstrated.
  • Conceptual understanding and procedural mastery is applied to new content.

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How do I implement the strategy?

  1. Choose math big ideas that are foundational to the lesson and that represent understandings that can be applied across lessons (e.g. area).
  2. Explicitly teach the math big idea, linking it to previously learned information.
  3. Explicitly teach the target math skill within the context of the math big idea.
  4. Provide multiple practice opportunities for students using the Big Idea with the new math skill you taught.
  5. Apply the math big idea to the target math skill using a variety of problem solving situations.
  6. Pair a visual cue with each math big idea (e.g. a picture of an array for the Big Idea of "area").
  7. Post the visual cue along with one sentence describing why the big idea is important.

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How Does This Instructional Strategy Positively Impact Students Who Have Learning Problems?

  • Focuses teaching and learning by clearly defining essential concepts.
  • Facilitates recall by reducing the amount of essential information.
  • Provides connections and linkages across discrete math skills.
  • Enables learners to understand that math is predicated on some key foundational concepts that can be used in a variety of situations.
  • Makes the logic and linkages of math concepts clear.

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Additional Information

Research Support for the Instructional Features of this Instructional Strategy: Carnine (1997); Kameenui & Carnine (1998); Miller & Mercer, 1997; NCTM (2000).

Example lesson for teaching math big ideas

The following is an example of a lesson introducing the area model of multiplication for single digit whole numbers for students who have experience using geoboards to make arrays and are at the representational stage of understanding.


1. Provide students with geoboards and have them count the number of places in several arrays (2 x 3, 4 x 5, 1x 7) using word problems such as: I have 2 brothers. Each brother has three pokemon cards. How many cards do we have combined together?

2. Have students do the same exercise using a paper array.

3. Explain that the purpose of the lesson will be to use an array or area model to combine number groups (sets). This is also called multiplying.

4. Tell students that using an array or area model will help them with all kinds of multiplication problems they will have.

Teacher Demonstration and Modeling:

1. Using an L shaped mask as described below, show an array boundary. Explain that the dots inside show the area.

2. Demonstrate how to count vertical and horizontal rows and the area inside the array with "think alouds"

3. Show the transfer between the array and a written multiplication story problem."Mary’s classroom has 4 rows with 6 desk in each row. How many desks are in the classroom?" Write the problem 4 x (of) 6 while thinking aloud: "I have 4 groups of 6 desks so I _____ desks in all." Show the array 4 by 6, and how it shows 4 rows of 6 groups. Count the number of dots in the array.

4. Continue to demonstrate different problems using scaffolding and "think alouds". (See the instructional strategy, Scaffolding Instruction, for more guidance.)

5. Check student understanding by asking questions such as: "I’m using an area model to multiply. The area is the space inside my numbered lines. Where is the area?"

6. "I’m showing you how to combine groups of numbers, that is a math operation called multiplying. What math operation are we doing?"

7. Use non-examples to check student understanding. Write the problem 3 x 2 on the board, but make an array of 4 x 2, or count the dots outside of the area, etc.

Guided Practice/Scaffold Instruction

1. Ask students to show problems using the L mask and paper arrays while providing assistance.

2. Provide multiple opportunities to use the array and provide answers to problems moving from greater to less amounts of scaffolding.

3. Ask students to complete the sentence: We can use an area model to solve _______ problems (multiplication).

Independent Practice

1. Check student understanding by providing multiple problems to complete independently.

2. Have them both demonstrate arrays for given problems (2 x 4 = 8) as well as solve problems (2 X 4 = ___).

3. Have students explain what the array shows (the area inside), and which math operation they are demonstrating (multiplication). (See the instructional strategy, Providing Structured Language Experiences, for more guidance).

4. Post a visual array with an illustrative story problem and the math sentence along with a written statement such as: "We use the area model to combine groups of numbers. This is multiplying."

See examples:

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