Teach basic facts using fact families for reinforcement. While students are learning that 3 times 6 equals 18, they can also see that 18 divided by 6 equals 3. Division is the inverse, or undoing of multiplication and not a new set of facts to learn. Give students three related numbers such as 4, 6, and 24 and have them create the four basic multiplication and division facts using the numbers.
Start with concrete representation of concepts before moving to the symbolic, abstract version. Through modeling, constructing and building, students will develop an understanding of geometric relationships. Have students create shapes according to specific instructions. For example, direct students to create a quadrilateral, or four sided shape with two sets of parallel sides and two sets of perpendicular sides. Students should correctly draw a square or rectangle. Then change the directions to include different types of angles to model parallelograms and trapezoids.
Separate students into small groups to work together on strategies to solve a math problem given by the teacher. Problems need to be interesting and challenging in order to engage students. Examples include working with data analysis to measure different heights of students in a group and constructing bar graphs to represent the data collected. Surveys can also be created to determine favorite ice cream or pizza toppings. Students can collect data from the class and create bar graphs to display the results.
Ask students to discuss their problem solving strategies encouraging students to communicate mathematically. Select problem solving activities that give students a chance to explore various strategies and formulate a plan. By putting their strategies in writing, teachers can assess conceptual understanding. Inefficient strategies should alert teachers that reteaching may be needed. Problem solving activities requiring students to explain how they got the answer help prepare students for the open ended questions that appear on standardized tests.
For example, direct students to count the number of total pencils in the classroom. Using the total, students can estimate the total number of pencils in the classrooms on the same floor, in the school and in the school district. Students can discuss estimation, addition or multiplication number sentences that were used to solve the problem.