Ensure that each student has a solid understanding of basic addition before attempting to teach partial sums. To do this, use flash cards with simple one to two digit addition problems to test the students knowledge of addition. If a student has trouble adding any of the problems, either teach him how to add by having him add together pennies, or provide him with practice problems if he just needs practice, but understands the concept of addition. Use pennies to teach by giving him two numbers to add together. Instruct the student to make two piles that represent each number, then combine the piles and count all of the pennies.
Let the students draw groups of kids completing various activities. Assign each student the responsibility of drawing one picture with a specific number of kids. Make sure to allocate your resources so that you have a total of 10 drawings with different numbers of kids in each drawing. Once completed, have the students group the kids on the board in order from least to greatest number of kids. Then, ask them to figure out the partial sum of the first four drawings by adding together the total number of kids. Remove the first drawing and then ask them to add the next four sets of kids together.
Write a set of numbers on the board; there should be at least 10 numbers in the set. Divide the classroom into two groups and ask each group to choose one member to come to the board. Tell the students to add together a partial segment of the sequence. For instance, ask them to get the partial sum of the first two terms in the sequence. The first student to get the correct answer will win a point for the team. Then, select a new group of students from each team to come to the board.
Give each student several colored blocks. For a good sample size, find a set of blocks that has at least five different colors. You may also use math chips or any other set of tokens that has a variety of colors. Randomly give each student a different number of each set of blocks. For instance, you might give one red, three blue, seven orange, four yellow and five green. Just make sure that you don't give any student more than one set of the same number of blocks. Ask the students to put the blocks in order and then add the first three groups together. Then explain that they just added a partial sum from the entire sequence.