Multiplicative Comparisons

Happy New Years!  I hope that this year will be wonderful and fun! I can’t say that I am entirely excited to start after winter break, but I do love that we have a few solid weeks of school. It really feels like time to get to work.

One of my very favorite things about teaching is the problem solving that I get to do everyday. Last year I was teaching about how multiplication can be used to describe a comparison and it went pretty terrible. My kids were very confused, did not do well on several of my assessments, and weren’t having any fun. My team and I worked it out with some hard work and reteaching, but this year I was so excited to give the unit another try.

I think part of the difficulty in teaching multiplicative comparisons is it can be hard to show students how it is useful and applicable in their lives.  To help introduce the concept I listed a whole bunch of comparison facts on the board.  For example, the sun’s diameter is 400 times bigger than the moon’s or that an ant can carry 100 times it’s body weight.  I then showed my students a website done by National Geographic. It compares things to the size of a blue whale. They went crazy for this.  Using the website we wrote in their math journals comparison statements and equations.  For example for the screen shot below we wrote “the blue whale is 3 times as big as a school bus,” as the comparison statement.  Screen Shot 2015-01-04 at 7.42.08 PM

After this my students were ready to start making their own comparisons.  We started by comparing a glue stick to items in our classroom.  I passed out the glue sticks and they started measuring.  This allowed them to get hands on experience comparing sizes of things and using multiplication to discuss the comparison. They filled out a chart that helped them write the equations and comparison statements.

My students were then ready to start drawing and understanding comparisons they might see in homework.  We practiced this a lot in the next few days by completing charts.  We also played a game that is hands down my kids favorite math game so far this year.  We call it Snatch, but you might recognize it as Spoons.  Students play the game by passing around cards with with multiplicative comparisons models, statements, and equations.  They try to gain a match and then sneakily snatch a pencil from the center of the circle.  The person left without a pencil loses that round. It was a total hit in our room and they still often ask if they can play (this game, all the charts, and glue stick activity are available here).

Slide02Overall this unit went a million times better than it had in the past. I know my kids did much better on my unit assessments and I know they feel confident in the their skills.  I really feel like it was a teaching win.


Find ALL the Factors

Last year when I was teaching factors, I found myself having the same conversation over and over again. I would see a student who had missed a factor pair on a question and would ask them, “Did you find all of the factors?” They would usually say, a little unsure, that they did.

I wanted to help my students to organize their thinking on paper to help them find all factors. I wanted them to be able to confidently say they knew that they had them all.

I realized that if the number you are factoring is less than 100 you can check the numbers 1-10 and be sure that you found all the factors. Once a student gets good at doing this on paper they will be able to start doing it in their head.

Find ALL the FactorsTo set up the problem I write the number I’m factoring on top and list the numbers 1-10 in two columns underneath. Then I go through the numbers one at a time. If it is a factor I find its pair, if it is not a factor I cross the number out.

I teach my students different strategies to figure out if the number is a factor, and to prove their answers.

  • Multiplication facts (8×8=64 not 63)
  • Long Division
  • Skip counting
  • Divisibility rules
    • 1 is always a factor
    • 2 is a factor if it is an even number
    • 3 is a factor if the sum of the digits is divisible by 3
    • If the number is odd then 2, 4, 6, 8, and 10 are NOT factors
    • 5 is a factor if it ends in 5 or 0
    • 10 is a factor if it ends in 0

This year if a student was missing a factor pair I asked them to prove how they knew the numbers they crossed out were not factors. As they explain it to me I could correct misconceptions, and they had a strategy to find the missing factor pair on their own.

I created a practice page that has plenty of room for students to show their work. You can download it for free from my TpT store.Slide2

Elizabeth also has some great factor resources for sell here.

Place value with Infographics

In 4th grade we don’t spend a ton of time teaching place value. By then the hope is that most students will just need a review of concepts they have learned in past years. One standard that is on our core is to solidify understanding that each place value spot is 10 times bigger than the one to the right. I was looking for a way to really get my students engaged and decided to use some infographics. After a quick little internet search I found some that included some large numbers and that I knew 4th graders would LOVE.

So then the plan was to have students choose a infographic and find any two numbers that have at least one digit that is the same. Then they had to record the value of each digit and how they compare. I had each student record his or her findings on the place value practice sheet.

My kids loved this. They mostly loved reading all the fun facts, which my literacy self was totally okay with. It turned out to be a great way to access some big numbers.

I have made the student practice sheet available for free at my TpT store.

Good luck!.