120 ◆ Modeling Thinking
grade, students are expected to add sums within 100. This can be very
tricky to teach. Using number lines and number grids as scaffolds can
help tremendously.
With number lines, you want students to begin to compose and decom-
pose numbers. You start out with easy problems, and you scaffold up to
more difficult ones. So a starter problem might be: Susie had 10 lemons.
Her friend gave her 10 more. How many does she have altogether now? In this
type of problem, the children start jumping 10s quite comfortably. They
do this on the number grid as well, where they simply have to slide down.
After the children become comfortable skipping 10s, you introduce
some 5s. You might say: Susie had 15 lemons and her brother gave her 25
more. The children would then start at the large number and break the
smaller number up into 10s and 5s. So, they would jump 25 to 35 and
then 5 more. Once the children are really comfortable jumping around
between 10s and 5s, then you introduce some numbers where they have
to decompose into 1s.
5101520253035404550Figure 7.20
01020304050607080 10090Figure 7.21
Figure 7.22
Don’t just stop with whole numbers. Make sure that students have
fraction and decimal number lines, depending on the content that they
are studying. Have students engage in a variety of routines throughout
the week where they have to reason on the number line.
.10 .20 .30 .40 .50 .60 .70 .80 .90 1(^01) ⁄ 10 2 ⁄ 10 3 ⁄ 10 4 ⁄ 10 5 ⁄ 10 6 ⁄ 10 7 ⁄ 10 8 ⁄ 10 9 ⁄ 10 1
Figure 7.23