Kids Don’t Know Their Multiplication and Division Tables!

by Sam Frydman

Ditmas Junior High School

Introduction

The Common Core Standards are the standards we use to make sure students are making adequate progress – that they are learning enough to be successful later in life. These standards are broken up by grade level, explaining what each student should know and be able to do once they reach a certain grade. For example, in eighth grade, students should be able to work with negative exponents such as 7^(-2). Sometimes students go above and beyond these standards, learning even more than the minimum requirements. Other times, their pace has been slowed so that they are not performing at grade level. The consequences of this can be severe, with students not having the skills they need to be successful in life.

One of the most basic skills that all students should acquire is 3.OA.7, “Fluently multiply and divide within 100… [K]now from memory all products of two one-digit numbers.” The “3” at the beginning of the standard means that this is for 3^rd grade, yet many 7^th graders in Mr. Frydman’s class still do not have their multiplication and division tables down! This will prevent them from doing very basic things later in life, like handling money, and will make it nearly impossible to enter some professions they might be interested in such as science, engineering, computers, accounting, and many others.

On a more relatable level, not knowing their multiplication and division tables by heart makes it more difficult to be successful in math class and to perform well on the state test. Topics that should be relatively easy, like reducing fractions, finding a unit rate, or filling in a proportional table, are made more difficult when students cannot remember 8x7 or 42/6, and students miss out on the feeling of success they could have had if they had only mastered more basic skills.

Task

You are a public policy maker in the Department of Education. You have been concerned that students are not learning their multiplication and division tables well enough. Your task is to create a PowerPoint presentation which will systematically go from defining the problem to picking the best solution to it. Each slide of your PowerPoint is explained in the next section.

Process

You will work in groups of three or four to complete the PowerPoint. The slides are as follows…

Slide 1 – Define the problem:

On this slide, please explain what the problem is and how it affects students.

Slide 2 – Gather the evidence:

In the beginning of the year, students were given a test on multiplication and division. The test consisted of 100 questions (50 multiplication and 50 division) and students were given 10 minutes to complete it. The scores from two of Mr. Frydman’s classes are shown below.

89 44 74 55 97 79 64 54 99 26 100 47 81 72 69 100 85 71 100

38 7 37 67 36 33 100 65 48 91 44 87 77 37 87 98 99 100 98 87

99 40 75 90 81 52 28 100 95 32 67 56 96 36 47 100 24 99 65

87 48 96 72

Using this data, create a histogram that visually depicts the layout of the scores. Count how many students got between 0 and 10, between 11 and 20, and so on, and draw a bar above that section on the x-axis to indicate the number of students who got that score.

Slide 3 – Identify the causes

Read through the following websites and identify some of the causes for students not knowing their multiplication and division tables. AS YOU STATE THE CAUSES, MAKE SURE TO GIVE CREDIT TO THE AUTHOR (say where you got it from).

https://expattutor.wordpress.com/2011/07/14/why-so-many-elementary-students-arent-mastering-basic-math-facts/

http://triplehelixblog.com/2011/09/multiplication-tables-dismal-state-of-u-s-mathematics-education/

Slide 4 – Evaluate an existing policy

Existing policy

Talk about how you and the other people in your group learned your multiplication and division tables. Did your teachers make you stand up and recite them? Did you recite them as a class? Did you use worksheets, flashcards, or computer software? Did you sing songs or read poems? Did your parents help you? If so, how?

Evaluate

After you write about how you learned them, discuss how effective those methods were. Do you really know your tables now or do you still struggle? If some members of your group struggle and some know them well, that’s ok. You can compare how each of you learned your tables to decide which method is the most successful.

Slide 5 – Develop solutions

Look at the following websites that discuss or show some ways students learn their multiplication and division tables. On this slide, explain four or five of the methods that you like. AS YOU EXPLAIN THE METHODS, GIVE CREDIT TO THE AUTHOR OR SITE (say where you got it from).

http://www.mathopolis.com/games/math-trainer-all.php

http://www.multiplication.com/teach/teach-the-times-tables

http://www.theguardian.com/education/teacher-blog/2013/apr/29/times-tables-teaching-resource

Slide 6 – Select the best solution

Place the methods you found for Slide 5 on the Feasibility/Effectiveness chart. Some methods might be in the same box on the chart. Underneath, justify all your placements. That means explain why you put that method in that box on the chart. Finally, decide on what you think the best method is based on your chart.

Evaluation

Here’s the rubric I will be using to grade your PowerPoint. As you work on this project, refer back to the rubric to make sure you are doing what you need to. That way, your grade won’t be too much of a shock! You can ask me if you have any questions.

	3	2	1	0
Relevancy	The group stuck strictly to the topic of each slide, not veering off in different directions. Furthermore, ideas are clearly stated and easy to understand.	The groups stuck mostly to the topic of each slide. Ideas are mostly clearly written but are sometimes unorganized or opaque.	Slides are related to the topic but often veer into unrelated tangents. Ideas are difficult to understand.	Slides are unrelated to the topic. The intended message of the slides are lost.
Sources	Source information has been cited for all causes and methods used in Slides 3 and 5.	Source information has been cited for most causes and methods used in Slides 3 and 5.	Source information has been cited for some causes and methods used in Slides 3 and 5.	Source information has not been cited.
Completeness	All slides have been completed. Work on each slide has been completed as described in the instructions.	All slides have been completed. Most of the work on each slide has been completed as described in the instructions.	One or two slides are incomplete. Most of the work on the completed slides has been completed as described in the instructions.	Three or more slides have not been completed.
Grammar and punctuation	Grammar and punctuation is nearly perfect.	Grammar and punctuation is very good, with a few mistakes.	There are many grammar and punctuation mistakes, occurring on multiple slides.	Grammar and punctuation is poor enough that the project is difficult to read, with the message of the project possibly being lost.

Conclusion

This project should make you more aware that a lot of students need to learn their multiplication and division tables better. You have looked at the data concerning where students stand now, looked up possible causes and solutions, and evaluated the solutions based on feasibility and effectiveness. As you work on your PowerPoint, and even after you’re done, think about the following questions. We will have a class discussion when your projects are finished.

How can not knowing multiplication and division facts affect learning in other areas of math?

Can not knowing multiplication and division facts affect understanding in subjects other than math?

If you know your multiplication and division tables very well already, how long did it take you to learn them?

If you do not know your multiplication and division tables very well, how do you feel about that? Do you think you could learn them if you studied a little bit every day?

Can you think of any real world examples for which you must know your multiplication and division tables?

Multiplication and division are considered “basic skills” for math. What are some basic skills in your other subjects? What would it be like to not have mastered those skills?

Common Core State Standards

ELA (from Common Core State Standards)

7^th Grade Writing 6 - Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources.

7^thGrade Writing 7 - Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.

7^th Grade Writing 8 - Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

Social Studies (from New York State Social Studies Framework)

7^th Grade A5 - Make inferences and draw general conclusions from evidence.

7^th Grade B3 - Identify causes and effects, using examples from current events, grade-level content, and historical events.

Math (from Common Core State Standards)

6^th grade SP.4 - Display numerical data in plots on a number line, including dot plots, histograms, and box plots.