Time Frame: 5 class periods that run 15 minutes each.


Summary: At the conclusion of this lesson, students will be able to successfully multiply multidigit numbers using rectangular arrays, and a variety of mental math strategies.
Materials:
 base ten blocks
 crayons
 grid paper
 One Hundred Hungry Ants, Pinczes, Elinor J., Houghton Mifflin
Co.
Additional Resources
Lessons for Introducing Multiplication, by Marilyn Burns (Math Solutions
Publications)
Lessons for Extending Multiplication, by Maryann Wickett and Marilyn
Burns (Math Solutions Publications)
Attachments
Background For Teachers: Multiplication instruction traditionally has focused on two objectives: memorizing
the multiplication facts and using one consistent, standard algorithm to multiply
multidigit numbers. Knowing the multiplication facts and computing efficiently
are very important goals, but a deeper conceptual view of multiplication is
essential. These lessons offer concrete experiences to minimize the risk of
students learning how to do procedures or learning facts without understanding
why they make sense. The students will develop key mathematical understandings
through building rectangular arrays to help them visualize that a problem like
4 x 27 can be considered (4 x 20) + (4 x 7). They will mentally multiply multiples
of 10 or 100, and use the distributive property to calculate
products.
Students in third grade have developed the multiplication concepts with a variety
of concrete methods and can relate the representation to an algorithm. Fourth
grade will extend this foundation by multiplying multidigit numbers using rectangular
arrays, and a variety of mental math strategies. The students will be able to
explain how multiplication relates to rectangular arrays, multiply mentally
by multiples of 10, and use the distributive property to calculate products.
These activities will take several weeks to complete. Allow ample time for students
to build rectangular arrays and determine the area before making a connection
to the algorithm.
Intended Learning Outcomes: 1. Demonstrate a positive learning attitude toward mathematics.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematical situations. Instructional Procedures: Invitation to Learn
Read One Hundred Hungry Ants.
Instructional Procedures
 Have student make an 8fold book (see handout). Challenge them to draw
all the different ways the 100 ants could travel, staying in equal rows.
 Build various models of two digits x one digit (e.g., 4 x 13), draw on
grid paper, and connect to the algorithm. Explore with the students ways to
find the area of rectangles using base 10 blocks and making smaller rectangles
with groups of 10’s and 1’s on grid paper.
 The above example shows 4 rows of 10 plus 3. There are 4 groups of 10 which
is 40, and 12 ones altogether; 40 + 12 = 52. This activity uses the distributive
property: 4 (10 + 3) = (4 x 10) + (4 x 3). The ability to break down a large
problem into smaller, more manageable ones is vital to conceptual understanding.
 Build various models of two digits x two digits, draw on grid paper, and
connect to the algorithm. The example below shows the area representation
of 13 x 12. This rectangle is composed of 4 smaller rectangles. A is composed
of a hundred’s board, B and C are composed of tens, and C is composed
of singles. The area of the original rectangle is determined by adding the
areas of rectangles A, B, C, and D. When moving to paper and pencil, have
the students record the partial products to help illustrate the steps involved
in the standard algorithm and bring meaning to this process. It may be helpful
to have the students use base 10 grid paper. Have students practice the following
problems: 15 x 14, 12 x 18, 16 x 16, 11 x 14.
Have the students build 12 x 24 with their base 10 blocks, sketch, and find
the area using partial products. The example below shows 2 hundreds in the
darker shaded region, 8 tens in the lighter shaded region, and 8 singles in
the unshaded area. Therefore the total area of the rectangle is 288. Have
students build rectangles to help find products to various problems (i.e.,
16 x 23; 22 x 27; 21 x 19; etc.)
Curriculum Integration
Math/Science—Have students collect data on dinosaurs. They will need to
record the height and length of each specific dinosaur. Determine the area that
each dinosaur would take up. (e.g., a Tyrannosaurus is about 40 feet long and
20 feet high, 40' x 20' = 800 sq ft.). Use grid paper to show each rectangular
array. Students will take their grid paper diagram outside and use chalk to
roughly sketch the dinosaurs actual size using the dimension boundaries determined
from research. As the groups finish their sketches, have them write the dinosaur’s
name and dimensions near the sketch. Have students write in their journal about
what may have surprised them about the reallife size of the dinosaurs.
Attachments
Extensions: Possible Extensions/Adaptations
Have the students mentally solve the problem 4 x 27, then as a group, share
their strategies for finding the answer. Have the class solve 6 x 32 using each
of the student’s methods.
Homework & Family Connections
Teach a member of your family how to multiply using partial products. Return
a note indicating the shared mathematical experience between the family member
and the student.
Assessment Plan: Have students multiply twodigit numbers through building, sketching, and
showing the computation with partial products.
Author: Utah LessonPlans
Created Date : Aug 29 2003 08:54 AM
