Number sequence problems are designed to introduce students to the number system of mathematics so that they are familiar with the characters of numbers and the order in which they go. Examples of problems include asking students to count the numbers one through ten, going upward and downward, and later 11 through 20, counting even numbers from two to 20, and counting odd numbers from one to 19. Eventually, try counting by ten from ten to 100 and backward once students have mastered the smaller numbers.
After students are sufficiently familiar with the concepts of the numerical system, they can begin to work on addition problems. Students should start with simple two-number problems using lower numbers. This allows them to use their fingers as an adding tool, before moving toward problems with larger numbers and three or more numbers in the equation. Examples of problems include 1 + 1, 2 + 2, 5 + 2, 6 + 7, 10 + 4, 20 + 3, 33 + 44.
Soon after introducing addition, students can begin to work on subtraction. As with addition, students should start with simple two-number problems using lower numbers. This allows them to use their fingers as an subtraction tool, before moving toward problems with larger numbers and three or more numbers in the equation. Examples of problems include 1 - 1, 2 - 1, 5 - 4, 7 - 2, 10 - 4, 25 - 12, 45 - 23, 76 - 54.
Students typically begin to learn multiplication in the third grade, as it is more complicated than either addition or subtraction. They can no longer use their fingers as a tool, and instead should use multiplication tables as a tool when first learning how to multiply. Examples of problems include 1 x 1, 1 x 0, 2 x 1, 2 x 2, 3 x 5, 6 x 7, 8 x 2, 5 x 15, 15 x 10, 20 x 5, 40 x 35.
As with multiplication, students also typically begin to learn division in the third grade due to its relative complexity, and division tables should be used as a tool for first-time learners. Examples of problems include 1 ÷ 1, 2 ÷ 1, 9 ÷ 3, 16 ÷ 8, 42 ÷ 6, 100 ÷ 10, 200 ÷ 20, 54 ÷ 8, 99 ÷ 9.