Spill the Beans

Est. Class Sessions: 2

Developing the Lesson

Part 1: Group Beans to Count

Leftovers and Ones. In previous units, students have used the term "leftovers" to refer to the single items that remain when grouping and counting by tens. In this unit, we begin referring to these as "leftover ones" or simply as "ones." Start using this terminology in your discourse with the students but do not demand that they immediately make the language change. As they get used to hearing the term "ones" and as they continue to build their understanding of place value with tens and ones, the change will occur naturally.

Distribute blank paper and 40 to 70 beans to each student pair. See Materials Preparation. Ask each pair to count the number of beans in their pile. Ask students to record the number of beans counted on the scrap paper. Display the Spill the Beans Data Table Master and have each student pair report their total recording each in the fourth column, Number.

Ask students to explain how they counted their beans and what problems they had, if any, in counting them. Most students will have counted by ones, although a few pairs may have grouped and counted by twos, fives, or tens. It is expected that some pairs will have had problems organizing and counting the beans. Ask students whether their counting experiences were easy or difficult and why.

If no students used the strategy of counting by tens, remind the class of previous experiences in which they grouped and counted by tens (for example, Unit 5 Grouping and Counting). Point to 38 on the number line. Have students count up to 30 by tens, then count on by ones. If some students used this strategy for counting their beans, encourage them to discuss how it was helpful. Have those students demonstrate how they counted by tens to count their beans. Then have the rest of the class use the number line to count aloud by tens and leftover ones to the same number.

Lead a discussion comparing counting by twos and fives to counting by tens and leftover ones. Begin by displaying a collection of beans.

Using 43 beans, for example, ask questions similar to the following:

What would be a good way to count so many beans quickly and accurately? (Go by twos or fives maybe.)
Would counting by ones be quick and accurate? (It would work but it could take long and you could get lost as you count.)
Let's try twos. Can you tell easily and quickly how many groups of two and how many leftover ones there are? (It looks like a lot of twos but I see one leftover. I have to count the groups slowly to be sure.)

Provide two copies of the Ten Frames Master to students who may benefit from a tool to help facilitate organizing their beans into groups for counting.

Move beans into groups of five with three left over.

You also suggested counting by fives. Can you tell easily and quickly how many groups of five and how many leftovers there are? (There are less groups now so it would be faster to count; it looks like more than five groups, and I see 3 ones. We could count by fives faster than counting by twos.)
Is there a larger group I can use to count the beans more accurately and more quickly than fives? (tens)

Move the beans into groups of ten with three ones left over.

Now can you tell quickly how many beans there are? (There are only four groups of ten and three leftover ones. So that's 10, 20, 30, 40 and 41, 42, 43; 43 beans.)

Follow up the discussion by asking all pairs to go back to their beans and group them by tens. Have each pair report the total number of groups of ten and the number of ones left over. Record their answers on the display of the Spill the Beans Data Table as shown in Figure 1.

Use a 100 Chart to Group and Count. Display the 100 Chart and have students look at the 100 Chart page from the Reference section of the Student Activity Book. Ask them to find their individual totals on the 100 Chart.

Ask:

Describe how you found your number on the 100 Chart. (Answers will vary.)
How is the 100 Chart like your groups of tens and leftovers? (Each row is a group of ten; the leftovers are in the next row, but they don't fill a complete row.)

Using one student's total, (i.e., 43), ask how many groups of ten are in 43 and how many ones are left over. At the same time show on the display that it is also 4 complete rows on the 100 Chart with 3 more in the next row. To underscore the connection, have other students come to the display and use their totals to say aloud the same connections between the groups of tens with leftover ones and the full rows of ten with a partial row on the 100 Chart.

Ask each student pair questions similar to the following:

How many beans in all did you count? (43)
How many groups of ten and how many leftover ones is that? (4 groups of 10 and 3 ones)
How many whole rows on the 100 Chart and how many on the next row is that? (It is 4 whole rows and 3 ones on the next row.)
Show us the number on the 100 Chart. Let's all count aloud to 43 by tens and leftover ones on the 100 Chart. (10, 20, 30, 40, 41, 42, 43)

Have each pair of students count several collections of beans as time allows and record the results on their Counting Beans Data Table, then locate each total on their 100 Chart. If students are slow to grasp the grouping concept, they will have several additional experiences in this and later units to reinforce the connection between grouping, names, and location on the 100 Chart.

Assign the Group and Count Homework Master. Discuss students' counting experiences when they return their homework. Invite them to tell what they counted and to share problems or successes they had.