PICTORIAL MODEL MATH HOW TO

Go through several examples of having students add (you can give word problems) and have them demonstrate it with their unifix cubes. When students explain that it means putting two amounts of something together and getting a new total or amount, ask them how they might show that using unfix cubes. Let me walk you through some examples of what that might look like.Ĭoncrete: Have a discussion with students about what it means to add.

PICTORIAL MODEL MATH HOW TO

Using the CPA Approach to teaching students how to problem-solve will be a game-changer.

One of the greatest struggles I hear that other 3rd grade teachers have is with problem-solving. This allows students to make strong links between each stage. In this stage, students are using numbers to solve problems.Īlthough the CPA Approach has three distinct stages, teachers should be using all stages within one lesson. Once students have grasped an understanding of the concept through concrete materials and pictorial representations they can progress to abstract learning. Without this step, students can find visualizing a problem very difficult. Some teachers choose to skip over this step, but it is an important bridge between concrete learning and abstract learning. Students are no longer using the manipulatives but still are supported by the drawing. Pictorial learning involves drawing pictorial representations or sketches. Once students feel confident in concrete learning they can move to pictorial learning. Over the years, I have found that when I’ve used manipulatives to let students truly understand what they were doing and make connections, this helps them learn the standards the best. It’s their first experience with these concepts and they have a difficult time jumping into the math workbooks because the math is so abstract. In the 3rd Grade, many of the math standards are NEW to our students. As students work through math problems using manipulatives, teachers are able to observe and gain a greater understanding of misconceptions and to analyze students' depth of understanding. One benefit of concrete learning is it promotes discussion, which allows students to talk through and explain math concepts. However, concrete learning is equally important with older learners as it is with younger learners! ALL students benefit from learning math concepts in a concrete way, as opposed to just memorizing a procedure.

T here is a common misconception that older students do not need to use manipulatives and that they are just for the younger grades. The CPA Approach makes learning math accessible to all students, including those with math learning disabilities. By using concrete materials students are able to ‘see’ the math, and make sense of what is happening. Math is abstract and can be confusing for students! That's why providing concrete learning is so important in teaching elementary math. It is sometimes called the “symbolic” stage.

It is sometimes referred to as the “seeing” stage.Ībstract: Solving math problems using only numbers. Pictorial: Using drawings to solve math problems. This is a ‘hands-on' approach using real objects and it is the basis for understanding math concepts. It’s learning that transitions from concrete materials, to pictorial representations, to abstract symbols and problems.Ĭoncrete: Using physical objects to solve math problems. The CPA Approach builds on a child's existing knowledge by introducing abstract concepts in a concrete and tangible way. Jerome Bruner proposed this approach as a means of scaffolding learning. The CPA Approach was created by psychologist Jerome Bruner and stands for concrete, pictorial, and abstract learning.

Pictorial model math