Recently the first graders have been investigating math situations involving a Double Decker Bus. We read a story about a girl whose father drives one of these special buses, and we started to consider some of the mathematical implications of this bus scenario.
We noticed that our class MATH RACK is similar to a double decker bus in that it has two rows of beads, just like a double decker bus has two levels of seating:
(A side note about the math rack: this model supports the development of number sense and mathematical thinking. In first grade, the math rack particularly helps to highlight the importance of the 5 and 10 structure in counting and computing.)
Once we connected the Double Decker Bus to our math rack, we retold parts of the story using our math rack; for example, when there were 6 passengers on the top deck and 6 passengers on the bottom deck of the bus, we moved over 6 beads on the top row and 6 beads on the bottom row:
We talked about what we see on the math rack that helps us to quickly and easily count how many passengers are on the bus altogether. In the situation above, a student observed: “All the red seats are full. I know 5+5=10. Then I see there are also two white beads. So you can count those like 11, 12. So there are twelve passengers on the bus.” This discussion highlighted the ways that the 5 and 10 structures can help us to count and combine numbers.
The first graders had a chance to make their own math racks using beads, pipe cleaners, and cardboard. This activity helped to support the students’ understanding of the composition of the math rack. They carefully counted out 5 red beads and 5 white beads for the top and the bottom rows. Then they checked to be sure they had 20 beads all together on their math rack.
Next the students worked with partners to act out bus situations on their math racks. The students took turns being the bus driver, moving over beads on their math rack to show an arrangement of passengers on the bus, and then “driving by” their partner. The partner described what they saw: “I saw all the red beads and 3 white beads on the top.” We challenged the students to consider the questions: “How can you figure out how many passengers are on the bus all together? Is there anything that can help you to count easily?”
Most recently, the first graders have been considering different ways to show the same number of passengers on the math rack. We’re thinking about arrangements that make it easy to count the number of passengers (these arrangements use doubles facts as well as big “chunks” that are easy to count quickly) and arrangements that are difficult to count. The students worked in partnerships to show the same number of passengers in an “easy” way and a “hard” way.
We also played a matching game in which students found pairs of cards depicting the same number of passengers on the bus. Finding pairs of cards such as the one below provided opportunities for first graders to explore equivalent expressions: 5 + 3 = 4 + 4.
We are excited to explore more mathematical concepts connected to the Double Decker Bus in upcoming Math Workshops!
Anna Messing, M.A.T.
Grade 1 Head Teacher
This lesson was based on the Contexts for Learning Mathematics series by Catherine Fosnot and colleagues.