Goal 5 – Multiplying and Dividing with 8s
Concrete Routines
1)
Abacus Double-Doubles – have students represent an “8-times”
problem in 8 rows. Then have students
calculate 4 rows, and then have them double that. For instance, 8x6 would be modeled on the
abacus as 8 rows of 6. Then students
would calculate 4x6=24, and then mentally double 24 to get 48.
a. Note:
Be sure to have students share their mental math strategies for doubling
double-digit numbers such as 28 doubled for 8x7=2x4x7.
b. This same activity can be done using
counters and a 10x10 grid.
Representational Routines
2)
Eight-Patterns on the Hundred Chart:
Multiplication – have each
student place a marker on his/her individual hundred chart as 4s multiplication
problems are called out. Once students
have placed their markers, the answer should be provided and students’ strategies
for knowing without counting can be shared.
a. Ask students to predict and share
strategies for determining whether a product will be even or odd – over time,
the goal is for students to realize that an even number times any other whole
number gives an even product.
b. Encourage students to notice the repeating
pattern of 8s products ending in 8, 6, 4, 2, and 0.
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8
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16
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24
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32
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40
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48
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56
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64
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72
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80
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c. Encourage students to use 8x5 as a benchmark. Ask students to discuss how this can help
them know 8x4 and 8x6 without counting.
d. Also encourage students to use 8x10 as a
benchmark to assist with 8x9.
3) Eight-Patterns
on the Hundred Chart: Division
– have each student place a marker on his/her individual hundred chart as 4s division
problems are called out. Once students
have placed their markers, the answer should be provided and students’ strategies
for knowing without counting can be shared.
Abstract Routines – Clap Facts - Say
a fact such as “4 fives” or “28 divided by 4” and then use a hand signal for
wait. Give students 2 or 3 seconds to
process, and then clap your hands, at which time students will choral respond
with the answer.
