Addition of a two-digit number and a one-digit number: Using knowledge of composing-decomposing to understand the algorithm for addition with regrouping.
This mathematics resource kit uses video excerpts and written resources to support your reflection and learning about early elementary experiences that build fluency and flexibility with numbers. You can reflect alongside this lesson study team as they develop insight into helping students connect knowledge of single-digit numbers to addition of larger numbers.
Have you seen students in upper elementary or middle school use their fingers to calculate? What early elementary experiences would build fluency with mental calculation so students would not still rely on their fingers in later grades? Write down at least five experiences you know and then share your ideas with your colleagues.
The Kindergarten Japanese elementary mathematics curriculum devotes over 75% of total instructional time to numbers and operations. Games are a central feature of this instructional time and students build fluency composing and decomposing numbers to 5, then numbers to 10. In first grade, students expand their knowledge of numbers and operations by sequencing numbers and quantities up to 100 and noticing the relative magnitude of numbers. Students make units of 10 and recognize that 10 can be thought of as 10 ones or as a unit of 10, and they learn to think of teen numbers as ten and some ones.
The excerpts from Pine Trail Elementary School in Florida are from Ms. Hajdin’s first grade classroom and span over a 3-month period, from January through March, leading up to the Research Lesson highlighted in this resource. These first grade students have been using the Japanese Curriculum since Kindergarten.
The excerpts from Brookfield Elementary School in California and Harlem Village Academy in New York are taken from a series of lessons taught over several days by guest teachers Dr. Takahashi and Mr. Jackson, respectively.
Reflect with your colleagues: How might these experiences build students' fluency and flexibility with numbers? What experiences do you use in your classroom to build students' fluency and flexibility with numbers?
Excerpt 1: Two Numbers Together
Students shake 5 counters in a box, half of which is covered by an opaque lid. They look at the visible counters and predict how many counters are hidden behind the opaque lid.
Excerpt 2: 100 Chart Game, Ten Frame Game, Different Ways to Compose 9
This video shows the excerpts of 3 games. In the 100 Chart Game, students take turns rolling one die (then two dice) and advance their game piece the same number of spaces as the number rolled. In the Ten-Frame Game, students look at a partially filled ten-frame, and identify the quantity needed to make 10. In Decompose This Number, students find different ways to make 9.
Share with your colleagues what you noticed. After your discussion: Table 2 continued offers some examples of other teachers' ideas for excerpts 3 and 4.
Except 3: Single-Digit Addition with Sums Less Than 10loading video
Excerpt 4: Addition of Single-Digit Numbers with Sums More Than 10loading video
Murata, A., Otani, N., Hattori, N. & Fuson, K. (2004). The NCTM Standards in a Japanese Primary School Classroom: Valuing Student’s Diverse Ideas and Learning Paths. Chapter 7 in ‘Perspectives on Learning, 66th Yearbook’ by NCTM.
The lesson study team from Pine Trail Elementary School met weekly between January and March to investigate the sequence of experiences that would help all students see the power of making 10's.
Excerpt 5: Planning Highlights
Note: If you would like to see more highlights of this group’s planning meetings, a longer version is available here.
Excerpt 6: Starts With 8+6 and Review
What do you notice about the way the student uses the blocks at the board to replicate how she solved the problem using the make a ten strategy? What are the similarities and differences between the two strategies?loading video
Excerpt 7: 53+7
What do you notice about the different counting strategies students used during their work time at their desks?loading video
Excerpt 8: Sharing Strategies 53+7 at the Board
What do you notice about the choice of student strategies presented and their order of presentation?loading video
Excerpt 9: 42+8/94+6 and Relationship between 8+6 and 78+6
Notice how students react to the first demonstration of 78+6. What elements of classroom routines and lesson design help students make sense of a challenging new mathematical idea?loading video
Excerpt 10: Post-Lesson Discussionloading video
Pine Trail teachers conducted their work using Japanese elementary mathematics materials translated and tested as part of a federally-funded grant.