While computational fluency and fact mastery are encouraged, the essential question is how do the four basic operations affect numbers and when should they be applied? Students should understand that addition and multiplication increase values to reach a total amount. On the contrary, subtraction and division start with the total value and break them into to parts or decrease the value. Problem solving situations often involve selecting and applying one or more operations in one or more steps. There are a variety of strategies to use, such as mental math, paper and pencil and calculators. While calculators may provide an answer to an operation, the students must still understand and apply the proper operation needed.
Students should learn how geometric properties relate to the real world. Primary grade students can start to see geometric shapes, such as squares and rectangles, in their world starting with everyday objects, such as windows and doors. Intermediate students can advance to angles, polygons and pairs of lines. Understanding geometric properties helps to develop visual and spatial skills regarding two-dimensional and three-dimensional objects.
Math instruction generally starts with whole numbers before advancing to fractions and decimals. Students need to learn what are the properties of the whole numbers that are used to classify them. When exploring groups such as odd and even and prime and composite, students should begin to see patterns emerging. The same patterns will help students understand factors and multiples and develop fact mastery through patterns, not memorization. Proficiency with whole numbers will lead to a greater understanding of fractions and eventually, algebra.
Students should learn the importance of the concept of standard units of measurement. Before memorizing that there are 3 feet in a yard, students should think about what it would be like if there were not standard units. Measuring objects with your own foot instead of a standard foot results in inconsistencies. Cooking and baking with different amounts of ingredients results in problems. The purpose of standard units is to use an agreed upon measurement for consistency in building and creating.