
Bridges in Mathematics (
Parents and teachers may reproduce for classroom and home use.) ©The Math Learning Center
16
x 12
32
+ 160
192
1
Standard
Algorithm
Grade 5, Unit Two: Seeing & Understanding
MultiDigit Multiplication & Division
In this unit your child will:
• use multiplication and division facts through 12’s fluently
• multiply and divide by multiples of 10 (e.g., 40 x 70)
• review doubledigit multiplication using a variety of strategies
including the standard algorithm
• divide 2 and 3digit numbers by 1 and 2digit numbers
using a variety of strategies
• solve story problems involving multiplication and division with remainders
• measure using metric units of length (centimeters, meters, etc.), mass
(grams, kilograms, etc.), and capacity (milliliters, liters, etc.) and perform
conversions between units
Your child will learn and practice these skills by solving problems like those shown
below. Keep this sheet for reference when you’re helping with homework.
Problem Comments
Write the answer to each problem below.
37 30 40
x 10 x 12 x 20
370 360 800
Students are able to multiply fluently by
multiples of 10 when they know their basic
facts and when they have a solid
understanding of place value. Being able to
calculate mentally with multiples of 10 is
useful in and of itself, and it also helps
students estimate reasonable answers before
multiplying multidigit numbers.
Write a story problem for 12 x 16.
There are 12 bottles of juice in each case.
Luis bought 16 cases for his party. How
many bottles of juice is that altogether?
Make a labeled sketch to solve your problem.
12
10
2
10 6
16
10 x 16 = 160
2 x 16 = 32
160
+ 32
192
Luis has
192 bottles
of juice in
all.
It is important that students are able to
multiply multidigit numbers. They must also
understand the meaning of multiplication
well enough to write problems that can be
solved by multiplying.
In this unit, students review the strategies for
multiplying multidigit numbers they learned
in fourth grade: making sketches, finding and
adding partial products, and
using the standard algorithm. If
you look closely at the labeled
sketch at left, you can see how it
helps students understand why
the standard algorithm works.
Bridges in Mathematics (
Parents and teachers may reproduce for classroom and home use.) ©The Math Learning Center
Write a story problem for this division problem.
260 ÷ 20
Malia’s soccer team has 20 players. They have
$260 to spend on team shirts. How much can they
spend per shirt?
Make a labeled sketch on the grid below to
solve the problem.
20
200
13
200 + 20 = 220
220 + 20 = 240
240 + 20 = 260
20 x 13 = 260
so 260 ÷ 20 = 13
They could spend $13 on each shirt.
Students use rectangles to think about
division as the opposite of multiplication.
They also use the pictures to solve division
problems by adding equal groups until they
get to the dividend (the number being
divided, in this example, 260). This serves as
the foundation for the numerical methods
and algorithm they will learn in Unit Four.
There are 97 people on the swim team. They are
riding in vans to the swim meet in another city.
Each van carries 12 swimmers. How many vans
will they have to take?
8 vans can carry 96 swimmers because 12 x
8 = 96. There’s still one more swimmer, so
they need another van. They need 9 vans
altogether.
Students continue to solve division problems
with remainders, as they did in fourth grade
and in Unit One. In this unit, however, the
problems involve larger numbers.
A student who is fluent with facts through
12’s can apply that knowledge to solve this
problem. Other students might add up by
12’s or use a collection of related
multiplication facts to solve a problem like
this one.
Frequently Asked Questions about Unit Two
Q: Why do students use sketches to solve multiplication and division problems?
A:
Pictures help students see why different strategies, including the algorithms, work. An
algorithm is a set of steps for performing a particular calculation with specific kinds of numbers.
Algorithms are important because when they are used accurately and with understanding, they
are reliable, efficient, and universally applicable. Difficulties arise when students attempt to use
an algorithm for multiplying or dividing without having mastered the basic facts, when they
don’t understand why the algorithm works, when they forget the steps, or when they can carry
out the steps yet are unable to use their estimation skills to judge whether their final answer is
reasonable. The understanding of number relationships that students develop by using sketches
ensures that they will be able to use the algorithms correctly.
Q: When will students learn an algorithm for long division?
A:
In this unit, students review and consolidate methods for multiplying multidigit numbers, and
they also gain solid foundations for understanding long division. They will learn an algorithm for
long division in Unit Four.