In fourth grade, students compute and estimate whole number products of up to four digits by using mental math. Set up a time test in which your students mentally multiply numbers such as 62 times 100 or estimate products such as 48 times 99.
Fourth graders also explore the concepts of factors and multiples. Ask your students to list all the factors of 12 or name the first five multiples of the number 10. Using pencil and paper, fourth graders perform long division in problems involving remainders, dividends of up to four digits and single-digit divisors. For instance, consider division problems such as 884 divided by 7 or 1140 divided by 6.
Fourth graders learn the concept of fraction equivalence, that is, different ways of expressing the same fraction. For instance, 2/3 and 4/6 are equivalent fractions, so have students name other ways in which these fractions could be written. Students also need to know how to compare and order common fractions. Using a number line, have students place the fractions 3/4, 1/2 and 2/3 in the appropriate order. Encourage children to use visual aids to help with this task. Some may benefit from drawing a picture of a pie.
Fourth graders also learn how to add and subtract fractions with common denominators, such as 5/7 + 1/7. They convert between fractions and decimals involving tenths and hundreds; for example, have your students write 0.7 as a fraction or 80/100 as a decimal.
Students use formulas to calculate the area and perimeter of rectangles. Ask them to use the area formula, length times width, to find the area of a rectangle with a length of 13 and width of 11. Fourth graders must recognize relative sizes of measurements within a given unit system. To practice this skill, have them determine which is larger -- a meter or kilometer. Then ask students to convert 0.004 kilometers to meters.
Introduce students to protractors and have them use these tools to measure angles. Students should be able to visually classify angles as being either acute, right or obtuse. Draw a 40-degree angle on the board and ask the class what type of angle it is. Fourth graders should know the definitions of perpendicular and parallel lines. Ask them the term that describes two lines that never cross. Students use their knowledge of lines and angles to classify and compare shapes and explore symmetry. Ask them to make an observation about the angle measures of the corners of a rectangle.
A good way to help students develop proportional reasoning and understand the concept of fractions is the following project, which involves chocolate. Set up three tables or desks, leaving enough space for students to gather around each. Put one candy bar on the first table, two bars on the second and three bars on the third. Have children exit the room and re-enter one at a time. Each child should go to the table where she thinks she'll receive the most chocolate, assuming that the chocolate will be evenly divided among everyone at that table. Of course, the choice is easy for the first couple of students, but the task becomes more difficult further on. When a student chooses a table, have him write on a sheet of paper how much chocolate he expects to receive, revising that amount when a new student joins his table.
For a project tying together measurement, unit conversion and fractions, have students survey one another's heights. Have students use rulers, yardsticks or a combination. After all the children have been measured, have students express the heights in inches, feet and yards. Then have students gather height data from the class as a whole, determining what fraction of the class is exactly 52 inches, what fraction of the class is over 56 inches and so on.
These are just a few ideas; the list of projects is endless. For instance, when teaching symmetry, try a craft in which students make cut-out snowflakes. Or when discussing arithmetic of large numbers, have students design a budget taking into account factors such as salary and housing costs.