Geometric as well as number situations should be created. If given opportunities to reason from graphs about interesting situations, students can develop an appreciation for the problem-solving potential of making, using, and talking about graphs. The question becomes, Fig. Investigating graphical representations and their relationships to algebraic representations can give students a real sense of the dynamic relationship between the variables. Such problem settings also allow students to reason directly to, and hypothetically from, graphs.
Students can develop their spatial reasoning abilities in a variety of interesting settings.
They can gather a collection of small objects, such as spools, golf balls, small footballs, small cans and bottles, and foam cups, and then try to draw what they think the shape of the shadow of each object might look like. Relating the size of the shadow to the size of the object also allows the use of proportional thinking. Reasoning about what is happening and why should be a constant part of the study of mathematics. Students in grades 5-8 should explore mathematical reasoning through problem situations that are appropriate to their ages and interest.