2. Table of Contents
Rationale
Curriculum Objectives
Base-Ten Materials
Two-Digit by Two-Digit Multiplication
Student Lesson
Let’s Journal!
References
3. Rationale
Many students reach middle school without
solid grounding in the concepts they need to
succeed in more advanced mathematics.
Multiplication is one such concept.
Using models to form arrays can help students
to ‘see’ multiplication and work through
problems with greater understanding of the
math behind the numbers.
4. Curriculum Objective
Grade 5
N5: Demonstrate an understanding of multiplication
(2-digit by 2-digit) to solve problems.
Achievement Indicators:
1. Illustrate partial products in expanded notation
for both factors.
2. Represent both 2-digit factors in expanded
notation to illustrate the distributive property.
5. Curriculum Objective
3. Model the steps for multiplying 2-digit factors
using an array and base ten blocks, and record the
process symbolically.
4. Describe a solution procedure for determining the
product of two given 2-digit factors using a
pictorial representation, such as an area model.
5. Solve a given multiplication problem in context
using personal strategies and record the process.
6. Base Ten Materials
Base-Ten Materials can be a great tool when reviewing
multiplication with students.
By creating an array with these materials, students can
‘see’ the numbers being multiplied together and the
area they form, which is the answer, or product of
the two numbers.
thinkmath.edc.org
10. Let’s Journal!
In your journals, answer the following question.
Explain your work using pictures and words.
While visiting my grandmother’s
farm this week-end, she asked me
to collect the eggs from the
henhouse. When I was finished, I
had collected 23 dozen eggs. How
many eggs did I collect in total?
11. References
Aims Multimedia (Producer). (1991). The Children's Encyclopedia of
Mathematics: A Thousand and One Naughts: Multiplying
Larger Numbers. [Full Video]. Available from
http://www.discoveryeducation.com/
The Department of Education New Brunswick: Educational Programs
and Services. (2009). Grade 5 Mathematics Curriculum. Retrieved
from http://www.gnb.ca/0000/anglophone-e.asp#cd on August
11, 2011.
Notes:
Clipart downloaded from Microsoft PowerPoint’s free clipart
library.
Photo used is royalty-free. A link is included below the photo for
the creator’s website.
Notas del editor
This presentation is geared towards teachers who are teaching/reviewing multiplication. It contains instructional slides, but also includes a video and some activities that could be used with students.
The curriculum objective and achievement indicators are based on the New Brunswick Mathematics Curriculum document for grade 5. However, this lesson could also be used to help students in middle school who have not yet attained the level of competency required in multiplication.
Teacher Notes:This video, retrieved from Discovery Education, is approximately 8 minutes long. It is a cartoon depicting a King with a problem to solve that involves multiplication. The solution is determined using base-ten materials and nicely demonstrates how an array can help to solve a multiplication question.The complete video could be shown or just the segment pertaining to arrays, depending on the amount of time available.
Teaching Notes:Explain how the number can now be decomposed and seen in pieces Write equations right on the diagram or use sticky notes with actual models! Ex: 20 x 10 = 200 20 x 7 = 140 4 x 10 = 40 4 x 7 = 28 , Therefore 200 + 140 + 40 + 28 = 408.A major benefit of this model…students gain an understanding of place value. For example, they are not just ‘carrying the 2….which is actually 20!Have students test the validity of their answer with estimation! Ex: 24 x 10 = 240 and 24 x 20 = 480….therefore my answer needs to be somewhere in between.Stress the importance of starting from where the student is in their understanding. If a student is still struggling with 1-digit by 1-digit, begin by building an array to show 4 x 7 (4 rows of 7). When the student is ready, move into 1-digit by 2-digit, then 2-digit by 2-digit, etc… Reinforce the importance of differentiating the lesson in such a way that all students are building their understanding of multiplication by beginning from what they know and moving forward. This often will mean that students are working on different problems all at the same time.
This activity is designed to be done in the classroom with students either working individually or in small groups. Teaching Notes:Students begin by building the array using base-ten materials. (Have students who are not ready for 2-digit by 2-digit start with easier numbers such as 1-digit by 1-digit or 1-digit by 2-digit).After building the array, students should record their work on chart paper and be prepared to explain their thinking to the class.Have several students explain their thinking using the models and/or their chart paper.Check for understanding.Have students choose at least 2 other numbers to multiply together in this way. (Remind them to explain their thinking.)
