Learning Benchmark Multiplication Facts for 2 and 5
Now that students have foundational
benchmarks learned for 10s and
products with factors of 5 or less, they
are ready to begin learning more
difficult facts,in reference to
the ones they have already learned.
In this lesson students learn to Reference Multiplication
Multiplication Benchmarks and use
the strategy of
More Area Compare to learn the rest
of their benchmark 2s and 5s
multiplication facts
(circled in black, right).
While some students may already be
able to do repeated addition or
skip counting, it is very important that
students learn the rest of their
multiplication facts using these
strategies and models.
Unit 15 strategies lay the conceptual foundation for division, fractions, and algebraic concepts, while repeated addition and skip counting do not.
Referencing
Multiplication
Benchmark Facts and
Using the Strategy
More Area Compare to
Learn Even More
Benchmark
Multiplication Facts
Students already know their
2s and 5s multiplication facts
for products of 25 or less. Now
they are going to learn the rest
of the 2s and 5s benchmark facts by comparing the new fact to a benchmark fact they
already know.
Strategy ONE: Referencing Multiplication Benchmarks
Strategy TWO: More Area Compare
In this next sequence of demonstrations and questions, students utilize both of these strategies. They take a multiplication benchmark fact they already know (5 X 2) and use it to compare to a new multiplication benchmark fact (6 X 2).
When students are asked to use the More Area Compare strategy by identify how much more the new fact is than the old fact. This is similar to the strategy used in Units 4 and 5 to compare a new math fact (9 + 2) to a 10s fact they already know (9 + 1) to determine which is larger. This is different in that instead of 1 more they are now identifying 1 more group or set.
Learning The Rest of the 2s Facts
SHOW students the rectangle for the benchmark fact 5 X 2 on the coordinate grid. Review what they already know about this
benchmark multiplication fact by
asking questions such as:
ASK What do you know
about this fact?
How much area does it cover?
So how many groups of
two do you use to build
this fact? (5)
How many squares
are in this rectangle? (10)
THEN ASK What if this
fact was now 6 X 2?
Would it be bigger or smaller than 5 X 2? (bigger).
Would it be more squares and a larger area, or less? (more).
How many more groups of squares would there be?
(one more group of two).
How would it be different than 5 X 2, and how would it
be the same?
So what would that look like when you build it?
(Instead of 5 groups of 2, we would be cutting out a rectangle made up of
6 groups of 2).
DO Make a rectangle to represent
the area for 6 X 2 out of a
contrasting color, and lay it under
the 5 X 2 rectangle to compare.
Note: Facts with factors above 5 can now
be cut out of neutral colors. You might
want to explain to students that once
we get beyond 5 it would make for
too many colors, and it will be
simpler to start using the neutral
color beyond 5.
SAY Let’s compare 5 X 2
with 6 X 2. Which one is
bigger, and covers
more area? (6 X 2).
How much bigger is it, and
how do you know?
(6 x 2 has one more group of 2s than 5 X 2, so it’s bigger by 2, since there are 2 in a group).
ASK So how many squares are in the new rectangle? (12)
How do you know?
5 X 2 is made up of 10 squares, and 6 X 2 has one more group of two than 5 X 2. So that’s 2 more and that makes 12.
DO have students continue this process with the 2s facts for 7 X 2, 8 X 2, and 9 X 2, comparing each new fact to the benchmark they just learned, as demonstrated below.
Note: Once the new 2s and 5s multiplication facts are learned, they become ‘benchmark’ facts students can use to compare to other new facts they’re learning over and over again. Once facts become benchmarks,, 2s and 5s facts with factors higher than 5 should be cut out in a neutral color like salmon; new facts students are comparing to the salmon facts should be in a contrasting color such as blue until they are learned.
SHOW students a benchmark fact
they already know and have learned
(6 X 2) by placing a rectangle to
represent it on the grid paper.
SAY Let’s compare 6 X 2
with 7 X 2.
DO Cut out a rectangle
to represent the new fact, 7 X 2,
in a contrasting color (blue)
and lay it underneath
the benchmark fact.
ASK So which one is
bigger, and covers
more area? (7 X 2).
How much bigger is it, and how do you know?
(7 x 2 has one more group of 2 squares than 6 X 2, so it’s bigger by 2 more squares, since there are 2 in a group of squares).
ASK So how many squares are in the new rectangle? (14)
How do you know?
6 X 2 is made up of 12 squares, and 7 X 2 has one more group of two squares than
6 X 2. So that’s 2 more and that makes 14.
Learning The Rest of the 5s Facts
The process for learning the rest of the 5x Facts is the same as the one you followed to learn the rest of the 2s Facts.
SHOW students the rectangle for the benchmark fact 5 X 5 on the coordinate grid. Review what they already know about this
benchmark multiplication fact by
asking questions such as:
ASK What do you know
about this fact?
How much area does it cover?
So how many groups of
five do you use to build
this fact? (5)
How many squares
are in this rectangle? (25)
THEN ASK What if this
fact was now 6 X 5?
Would it be bigger or smaller
than 5 X 5? (bigger).
Would it cover more area or less? (more).
How many more groups of squares would there be? (one more group of five).
How would it be different than 5 X 5, and how the same?
So what would that look like when you build it?
(Instead of 5 groups of 5, we would be cutting out a rectangle made up of 6 groups of 5).
DO Make a rectangle to represent
the area for 6 X 5 out of a neutral
color such as salmon, and lay it under
the 5 X 5 rectangle to compare.
SAY Let’s compare 5 X 5
with 6 X 5. Which one is bigger,
and covers more area? (6 X 5).
ASK How much more area
is it, and how do you know?
(6 x 5 has one more group of 5s than
5 X 5, so it’s bigger by 5, since there
are 5 in a group).
ASK So how many squares
are in the new rectangle? (30)
How do you know? 5 X 5 is made up of 25 squares, and 6 X 5 has one more group of t5 than 5 X 5. So that’s 5 more and that makes 30.
DO have students continue this process with the 5s facts 35, 40, and 45, comparing each new fact to the one they just learned, as demonstrated below.
SHOW students a benchmark fact
they already know and have learned
(6 X 5) by placing a salmon-colored
rectangle to represent it on
the grid paper.
SAY Let’s compare 6 X 5
with 7 X 5.
DO Cut out a rectangle
to represent the new fact in a
contrasting color and lay it
underneath the benchmark fact.
ASK So which one is
bigger, and covers
more area? (7 X 5).
How much bigger is it, and how do you know?
(7 x 5 has one more group of 5s than 6 X 5, so it’s bigger by 5, since there are 5 in a group).
ASK So how many squares are in the new rectangle? (35)
How do you know? 5 X 6 is made up of 30 squares, and 7 X 5 has one more group of 5 than 6 X 5. So that’s 5 more and that makes 35.
DO Have students make fact cards for these facts to save for future reference,
CONTINUE modeling these concepts many times and in many different ways. Continue to avoid focusing on multiplication and addition operations. Instead, focus on the area being built, emphasizing its area and shape: 8 strips of 5 make a rectangle of 40 squares.
Last revised 03/10/2010
Ó2010University Place School District. All rights reserved. The Math: Getting It Project is a Mathematics and Science (MSP) Partnership funded by the Department of Education. Partners: University Place School District (lead partner), Peninsula School District, and Fife School District; the University of Washington/Tacoma; and the Pierce County Staff Development Consortium, Pierce County, Washington.
For more information, contact the Math: Getting Project Co-Directors, Jeff Loupas or Annette Holmstrom ,
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