Estimate Sums Using Intervals. Read aloud the
story on The Children Who Traveled to Find a Hard
Problem pages and have students follow along in
their Student Activity Book. Then read the problem
in the Dinner Guests section. Begin the discussion
by asking students to estimate the number of plates
the family will need.
Point to the intervals on the chart and ask:
- What interval do you think the answer will be within? (11–20)
- Why do you think so? (Possible response: I know
that 16 is close to 15, and 15 + 5 = 20,
so I think 16 + 4 is about the same.)
Strategies to Use with Larger Numbers. Use the
display of the Addition Strategies Menu for Larger
Numbers in the Reference section of the Student
Activity Book to review addition strategies.
- Look at the Addition Strategies Menu for Larger
Numbers. As you try to solve the Dinner Guests
problem, think about how we can use the strategies
or tools on this menu to solve this problem.
Have students work in pairs to solve the problem
using various strategies or tools. Number lines, ten
frames, 100 Chart, direct modeling with counters,
and mental math are all appropriate strategies and
tools to use for solving this problem.
As they finish, ask students to demonstrate their
solution paths for the class. Use Sample Dialog 1 as
a guide for your discussion of strategies and tools.
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Use Sample Dialog 1 to guide your discussion of using strategies and tools for solving the Dinner Guests problem
on the The Children Who Traveled to Find a Hard Problem pages from the Student Activity Book.
Teacher: What is your answer and what strategy or tool did
you use to solve the problem of finding how many plates
they need for their family of 4 and 16 guests?
Jake: I used counting on. I put 16 in my head and counted on 4:
17, 18, 19, 20. It's just the same as counting on with small
numbers only you start with a larger number.
Teacher: Good, Jake! You can use counting on as a strategy
for this problem because you're only counting on 4
more. Who has a different strategy or tool?
Daniel: I used Making Ten. I know that
6 + 4 = 10 and 16 is 10
more than 6, so I added 10 + 10 = 20.
Teacher: Great thinking, Daniel! Who else used one of the
strategies or tools we used for smaller numbers to solve
this problem?
Ashley: I used ten frames. I filled one of the ten frames with
10 dots and then I added 6 + 4. That filled up two whole
ten frames or 20.
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Teacher: How is using ten frames for larger numbers like
using them for small numbers?
Ashley: If you have a number sentence like 34 + 3, you can
take the 3 tens out of 34 and fill up 3 ten frames and then,
just add 4 + 3.
Teacher: Nice answer, Ashley! Who else can explain a
different strategy or tool?
Javier: I used the number line. I made 1 jump of 10 and 6 small
jumps and 4 more small jumps.
Teacher: So, how can you use the number line for adding
larger numbers? If you want to add
43 + 4, how would
you solve that problem?
Javier: I could make 4 jumps of 10 and 3 small jumps and then,
4 more small jumps.
Teacher: Does everyone understand how Javier solved that
problem? We have good thinkers in our class. We can
use some of the same strategies and tools we used for
small numbers to solve problems with larger numbers.
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Choose one of the strategies from the Addition
Strategies Menu for Larger Numbers and ask students
to solve another problem using that strategy.
- If the family had 7 members and 13 guests came to
dinner, how many plates would they need? (20)
- Use the Making Ten strategy to solve this problem.
Adding Tens and Ones. Tell students that Tess
started thinking about the adults who thought this
was a hard problem.
- Tess started thinking about making harder problems.
She thought, "What would I do if I had a
really hard problem. What if I had 20 guests?
30 guests? 40 guests? How many plates would we
need with our family of 4?"
Ask students to solve Tess' first problem: if the family
is having a dinner party and 20 guests are coming,
how many plates will they need for their guests
and their family of 4? Tell students they can use
whatever strategies seem to be best suited to solve
the problem. When students finish, have them
explain their solution paths. Then have them solve
Tess' second problem with 30 guests and third problem
with 40 guests.
Pose several similar problems with one addend
being a multiple of ten (e.g., 20 + 7, 30 + 2, 40 + 3).
- Who can see a pattern in these problems?
(Possible response: It's like adding 10 plus a
number. When you add 10 + 7, you just change
the 0 to 7.)
- What would 20 + 7 look like if we were solving it
using ten frames? How many full ten frames is 20?
(2) Then we are adding 7, so 7 dots go in the next
ten frame. What's the total number? (27)
- Solve 20 + 7 on the number line. How do you think
the hopper should move? (Possible response:
Start at 20 and hop 7 more. Or make two big tenhops
and seven little hops.)
- Is the answer the same? How is solving the problem
on the ten frames like solving the problems on
the number line? (Possible response: It is easy to
see the 20 on the ten frame and then go seven
more, and it's easy to see the 20 on the number
line and go seven more. Or, the two ten frames
are like the two big ten-hops and then you go
seven more.)
Adding tens and ones. As students develop and explain their
strategies for solving problems with larger numbers, it is
important that they see and talk about the digits in the tens
place as tens and not ones. Students' explanations are likely
to be tentative and insecure at this point. Help them gain
confidence by referring them to the visual and concrete
representations that they have developed. For example,
students can visualize 20 + 4 = 24 as two full ten frames and
four more filled boxes in the next ten frame, two hops of ten
on the number line and four more hops of one, two rows on
the 100 Chart and four more, or two trains of ten connecting
cubes and four more. As students talk, encourage them to
use these images to talk about the twenty in 24 and relate it
to the representations—two full ten frames, two hops of ten
on the number line, two rows of ten on the 100 Chart, or two
trains of ten connecting cubes.
If students have trouble making connections between
the solution on the number line and the solution on
the ten frames, ask:
- Where is the 20 on the number line? Where is the seven on the number line?
- Where is the 20 on the ten frames? Where is the seven on the ten frames?
