5 class periods of 15 minutes each
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.
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)
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.
1. Demonstrate a positive learning attitude toward mathematics.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematical situations.
Invitation to Learn
Read One Hundred Hungry Ants.
Instructional Procedures
10 + 3  13  

x 4  
40  
+ 12  
52  
Curriculum Integration
Math/ScienceHave 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 dinosaurs
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.
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.
Have students multiply twodigit numbers through building, sketching, and showing the computation with partial products.