Multiples in a Minute

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Objective

Students will be able to construct and manipulate factors in order to look for and express regularity in repeated reasoning.

Big Idea

Understanding multiplication is repeated addition is the first step in understanding the concept.

Introduction

The focus of today's short lesson is on having the students list as many multiple of a number as they can in one minute - creating an array (3.OA.3, 4.OA.4 review).  The reason I use this lesson is because many students do not realize multiplication of basic facts is repeated addition, they just know the algorithm(4.OA.3.1).  I want them to understand multiplication, and its relationship to addition.

Thinking multiplicatively involves many different mathematical ideas as well as constructing and manipulating factors in response to a variety of contexts. Trying to teach students the entire concept is overwhelming, for students and for you as a teacher. This lesson responds to that complexity. It is simple to teach and easier to learn because it creates a graphic visual for students.

Students also need to review applying properties of operations as strategies to multiply and divide.   (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

The students end up with a bar graph displaying the multiples of "difficult numbers" and "easy numbers". We return to this conversation (building on prior knowledge) when we work on multiplying multi-digit whole numbers using the standard algorithm and at conferences when a student needs to practice their basic multiplication facts. 

This lesson is also handy when a fire drill or something else has interrupted your math time and there is only 20-30 minutes for math, or if you find yourself needing to fill time. 

Engaging Students with Inclusion

5 minutes

As my class settles in from morning recess, I ask students to talk at their tables about what they know about multiplication. This practice is "inclusion." I believe that by sharing and discussing the topic of the day with each other, students are preparing for our more formal class discussions.

Inclusion also has an emotional purpose. Do you remember, when you were a student, that child who was trying to hide from the teacher calling on them because they didn't have the answer? It might even have been you. Inclusion makes sure every child feels more prepared and has the experience of being listened to.

This is the beginning of the year, so there are procedures we are practicing about how to have a discussion in Learning Clubs:

  • Everyone needs a chance to participate at his/her fullest ability
  • Only one person can talk at a time
  • Individuals can pass on their turn to talk (absence of threat) but are expected to participate.
  • Giving the right to pass to a student allows think time and time to build an idea on something another student said. This lowers the affective filter and does not shut down a student for not having an immediate answer - they continue in the thinking part of the brain.


Students begin sharing what they now about multiplication with their Learning Club (table) and I overhear things such as,

"It is like adding the same number over and over."

"It is a short cut for addition."

"I practiced my multiplication over the summer and have gotten really good at it.  I can't wait to show Mrs. Skinner!" (Cycling 5th grader)

"I don't know my multiplication facts."  Another student replies "We did this activity last year and it helped me know which facts I needed to practice.  I wonder if I will need to practice the same ones. You'll see it will help you too."  (Cycling 5th grader to a 4th grader.)

Multiples in a Minute

15 minutes

At the beginning of the year, I use as many lessons with multiplication in as many different ways as I can.  This is because I teach a multiage classroom with 4th and 5th grade students.  The multiplication is a review and a calm introduction back into the classroom after summer for the 5th graders. For the 4th graders it is teaching them different multiplication strategies so they can help themselves improve. The area of improvement will show as a graph once the activity is completed.

After I acknowledged the correct comments I had overheard during the inclusion question - multiplication is repeated addition, it is a short cut for addition, it is faster than addition when using larger numbers. I reinforce the idea that multiplication is repeated addition.  I also bring in language arts and root word and affixes.  The multi in multiplication means multiple times. 

Students take a lined piece of paper, turn it sideways so the holes are across the bottom and write the numbers 2-12, skipping lines under the red line.  I then tell them they are going to be doing what they learned in Kindergarten but at a different level of speed.  I am going to time them for one minute to skip count by 2's while writing in in a column above the number 2 on their list.  We will then continue on until we have filled in all columns up to the number 12.  

Students will want to share how many or how far they made it on each number with their Learning Club.  I allow about 20 seconds for this between each number, and it takes me about that long to reset the timer on my iPad.  I say "Ready, Set..........(students stop talking and get pencils ready)....Start" and they begin listing the multiples of the next number.  We continue this way until the multiples of 12 are done.  I give a little extra time on the last few lists because by this time the students hands are aching. 

As they finish I let them talk in the Learning Clubs for about a minute.  I hear students saying "Wow I really did get better!" 

"But I still need to practice my 9's or use the shortcut on my fingers." I overhear another student tell this one "If you just add 10 to the number and then take away one you'll get faster." 

After the short table talk time I ask the students to share with the class what they noticed or learned from this activity.  I do this by tossing a koosh ball to one student who answers and then they popcorn it to another student to answer.

Some of the students pop-corned answers were:

"It turned into a graph like our Favorites Surveys. The ones that have more multiples are the easier ones and the ones with fewer multiples are the ones I need to practice."  This was said by a 5th grader who knew the term multiples - introducing it to the 4th graders who may have not heard it before.

"A lot of us at my table have more numbers in the first columns and fewer in the last columns, except for the 10s."  I ask students to raise their hands if they need to work on their 6s - 9s.  The majority of the class raises their hand and I see a feeling of more comfort that they are not the only one who is going to be working on the harder multiplication facts.  My purpose for this is to let students know that they are not the only one who needs to work for improvement.  This helps them take more charge of their own learning. 

Student Reflection

5 minutes

As always, the lesson closes with students reflection on their own learning. They do this through writing in their math journals. This gives me an ongoing assessment of what my students have learned and some insight into who they are, as people.

I ask my students to write a paragraph about what they learned about themselves and this activity.  I not only have an insight into their thinking but I also have an informal assessment on writing a paragraph. 

This first student not only figured out which numbers were hard for them to find the multiples of but they related the chart to a bar graph.  This shows me they are building on other lessons we had done in the first couple weeks of school. 

After reviewing this student's work I can see they understood the purpose of the math lesson but will need to strengthen their descriptive voice in writing.