Multiplication Strategies

This post has nothing to do with something new and brilliant I’ve discovered about helping students learn their multiplication facts. Instead, it is about my learning. About a year ago, I wrote this post: Times (x) they are a changing . . . .  It was a reflection on how and why I stopped doing timed multiplication drills. Back then, I learned from my students about what they needed. We began to work on our facts in a different way and I was excited about what I saw.

In no way did I throw the baby out with the bathwater. I still believe children benefit from knowing their multiplication facts. Especially if they know them “by heart” so the answer to 7 x 8 is as easily retrieved as a birth date. This allows them to use these facts easily and quickly as they work on more complex problems in the intermediate grades.

But one year later, what am I thinking? Watching my students approach their daily practice with multiplication facts, I remain absolutely convinced that timed drills are not the way to go. Why?

*The stress of “being timed” just completely shuts some learners down before they even begin.

*Timed drills have a “test like” vibe and everything gets quiet. The “talking through thinking” stops and often, so does the thinking.

*Timed drills highlight what you already know as a teacher. Some kids learn their facts almost instantly, some learn them with lots of memory work and some struggle no matter what. So why create a situation that highlights this? It doesn’t highlight learning.

*Creating a situation where memorization is the only route to success means not everyone has success

What do I do instead? 

*We spend a lot of time on the concept of multiplication. The symbol x is taught as “groups of” so we would read this math sentence 2 x 4 as 2 groups of 4. We draw pictures. We work with manipulatives. We play games. We build and draw arrays (with blocks, graph paper, rows and dots) We solve problems (using pictures or blocks, etc)

* We then move on to learning that there are strategies to answering multiplication questions – this comes from our observations, discussion and the patterns we notice as we go. I never teach “tricks” at this stage like “just add a 0 to the other number when you multiply by 10” I let students figure it out themselves so that the “trick” is connected to the concept. Not so it replaces it.  It sounds something like this: Student A says, “I was counting by tens to solve these problems (4 x 10 and 7 x 10) but then I noticed that all of the questions that are groups of 10 always end in a 0.” Student B concurs, “Yes! It’s kind of like because you are counting down the 100s chart at the end part where you are skip counting by 10s. So you can just put a 0 on the end of the other number.” Another child listens to this and looks confused. Student A and B get out blocks or the hundreds chart and show them with skip counting.  They try out a few more and boom, they have a strategy that now works for them. And, they all understand because they have made meaning together.

*While we continue using multiplication to solve problems and even move onto division concepts, we do a daily practice sheet that contains 16 multiplication questions. Students move through these sheets at their own pace. They can talk. They can ask for support. Some work with a partner. Some get out blocks and build arrays. Some skip count on their fingers. Some do what they know first and then add on another group i.e. “I know 5 x 6 is 30 so 6 x6 is 30 +6)

What is happening in the room that wasn’t back in the days of timed drills?

*Self talk. I often hear a child talking through the questions

*Talking together and building knowledge

*Discovering strategies and sharing them

*Recognizing patterns

*Time and space to think

*Confidence and competence develop together

*And multiplication facts begin to become known facts. For some it is many. For others,    just a few. Some children are working on learning the 6s and 7s. Others are working with 2s and 5s. Others know them all fairly well and get sheets with a variety of questions to practice. When they feel ready, they tell me they want to move on. Often it just clicks and a child ralizes that they “just know” many facts and they get very excited to learn more. The exciting thing is when they move on to a new set of facts and recognize that they already know many of them!

*Everyone is making progress and multiplication is something we feel confident about!

So fellow primary teachers, how do you deal with learning multiplication facts? Would love to hear how things work in your room.

Our week in pictures

Life has been busy at Seymour School! But lots of great learning and working together has been going on. Some highlights of the past week!

Buddy reading with our little buddies in Division 7 (K/1) is always a highlight of our week. This week we broke out the rhyme and repetition bin and enjoyed the repeating parts of stories we could share together.

Sometimes books call to you, "Come into the story!"

Sometimes books call to you, “Come into the story!”

In math we have been working on skip counting. We find that physically moving numbers into sequence helps us practice the patterns really well. With 25s, we chanted “25, 50, 75, double zero!”

Follow the pattern!

Our reading group shared a fantastic book called Clever Beatrice written by Margaret Willey and illustrated by Heather Solomon.

Clever Beatrice

As we read, we charted the character traits we noticed in Beatrice and at the end of the story, took turns sharing examples from the text that illustrated each point. Soon, we will be doing this with a partner and then eventually, on our own,  as we read a picture book.

Character Web

In Science, we have been studying structures. Today we learned some new vocabulary to help us talk about bridges: approaches, foundation, supports and span. The task was then to build a bridge using just blocks and rulers.

This group attempted to make the longest bridge possible and even test drove matchbox cars up the approaches and along the bridge.

Straight and long!

Another group wasn’t interested in the longest bridge, they were all about interesting! This bridge had multiple approaches and reinforced supports. (And options for multilane traffic)

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All over the classroom, bridge construction and team work could be observed. The adults loved listening to small group presentations about bridge design and how the groups worked together. One self assessment: “Next time, I will work harder at team work.” We really do depend on each other!

Bridges everywhere you look!

Happy Halloween!

What a fun and exciting day we had today!

We started with a spooky read aloud, The Soup Bone written by Tony Johnston and illustrated by Margot Tomes.

This book is about a little lonely old woman who goes in search of a bone to make her soup a little more tasty. No bones in the the cupboards or the drawers or on the shelves. Not one bone anywhere. So the little old woman decides to go digging for a bone. This struck us as quite disgusting! “Eeew! The bone will be dirty!” ” Will it be a dino bone?” “Maybe a skeleton bone?” Well a skeleton was exactly what she found. The little old lady shrieked and ran away. When the skeleton decided to “skittle- skattle” into the house, Markus piped up “So finally she’s got some company!” And as we read on, we decided this story was a friendship story after all!

IMG_1384Following a spooky story time in the library with Ms. S after recess, we did math.

Today it was Pumpkin Patch Glyphs. Everyone had to design a pumpkin in a way that answered four questions.

Then everyone else had to look at the legend to learn more about their classmates as they examined the features of each pumpkin: stem, eyes, nose and mouth.

For example,  someone who loves chocolate would have a pumpkin with triangle eyes.

Is your favourite treat chips? Well then circle eyes for you. Lots of fun to look at all of the pumpkins up on the wall and make conclusions – most people like scary costumes for example. Glyphs are a way of organizing and representing data!

Some completed pumpkins:

Hailey is a chocolate lover who is not so sure about pumpkin pie.

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Shae-Lynn does NOT like pumpkin pie and has yet to try pumpkin seeds.

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Truman likes sweet treats and strange costumes.

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In the afternoon, it was all about pumpkins!

These unsuspecting pumpkins donated by the Rotary Club . . .

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turned into fabulous jack o’ lanterns with the help of our Big Buddies from Division 1.

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Even a little bride on her way to a wedding stopped in to do some carving!

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Final results looked something like this: successful carving and a big mess 🙂

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Happy Halloween 2011!

The Lion’s Share

One of our read aloud stories this week was The Lion’s Share – A Tale of Halving Cake and Eating it, too written and illustrated by Matthew McElligott

A little ant is invited to a special dinner hosted by lion and she wants to make a great impression. She is appalled by the manners and behaviour of the other guests who all arrived late and ate their way sloppily through the meal. After dinner, lion brings out a large iced cake and tells his guests to help themselves.

Students were suspicious. “He is just going to fatten them up and then he’ll eat them all,” suggested Jeremiah. Ricky agreed but added, “He will need a pack to bring down that elephant!”

The animals each took half of the cake and passed it on. The pieces became smaller and smaller (1/2 became 1/4 then 1/8 etc.) until the ant received her piece and crumbled it while attempting to slice the tiny sliver into two. The animals all appeared offended, accusing the ant of not sharing. The ant, wanting to make up for her supposed transgression, offered to bake a special cake for the lion. Well . . . none of the other animals wanted to be outdone by the ant and begin to promise cakes as well – each offering to bake twice as many as the last offer.

“Wow! This is like math!” exclaimed Jenny as students began doubling the numbers to predict what the next offer would be. After each animal had made his or her offer, we added all of the promised cakes together using a variety of addition strategies. 511 cakes! (1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256)

“Why was each animal promising to bake twice as many?” someone asked. (It’s great when students get to use math vocabulary in a meaningful context as it is often the language and not the operations which throw them with word problems)

Students answered. “To show off.” “To beat the others.” “They are competing.”

“But the ant was just calm.” said Scott.

The rest rushed it and the ant’s cake was the best.” observed Kevin.

“The ant wanted to make it special but the rest were competing.” Jena agreed. We had a great conversation about quality vs. quantity.

Then the math thinking just began to flow. Alyson noted, “511 cakes would take more than a year to eat if you ate one cake a day.”

“But less than 2 years,” said Ricky. “Because if you double 365 and you get 300 and 300 – that’s 600 so you already know it is more than 511.”

A lovely read aloud that led to some spontaneous math thinking. Fractions. Doubling. Addition. And some pointers on table manners! What could be better?

Highly recommended.


It was spatial awareness day! How did we do?

Part 1

First, it was all about fractions. These activity sheets are from Math to the Max 3.

P1020905We have continued using pattern blocks to cover figures on the page and then trace what we’ve done. Students are being asked to think of covering a figure with blocks that represent a specific fraction but this doesn’t mean you can tell from the fraction how many of each block you will need. It is necessary to visualize the figure in thirds to complete this task. Look closely.

P1020910On this page (pictured right) students were asked to visualize the shape split in half. If a figure is half blue and half green, it might be one blue block and two green blocks, because two green blocks cover one blue block. When adding a red block, you then must add three green. So a figure can be covered in two red blocks and six green blocks and be 1/2 red and 1/2 green. Some of these took multiple attempts before they were figured out.

Part 2

Then, in the afternoon, we moved on to making a maps. The task? Create a map of the school yard from a “bird’s eye view” perspective. The criteria?

  • work cooperatively within a small group
  • use any flat objects you can find in the classroom to represent buildings, places, objects (Students used paper, base ten materials, rulers, pattern blocks, lego, etc)
  • no pencils or crayons allowed
  • be prepared to explain any parts of your “map” at any time
  • anything you take out, must be put away at clean up time
  • have fun!

The results were fascinating!

P1020938These students were able to “visualize” certain areas of the school grounds very easily. In the foreground of this photo you can see their earthquake shed, the garden, the garden bench.

The only problem? They couldn’t orient themselves clearly. Their garden area is actually where the brick building should be and on the other side.

There was lots of talking, lots of discussion, lots of flexibility around new ideas within this group but nobody could get a vision happening that everyone could understand. This task was harder than it first seemed!

P1020929This group worked very well together. If you listened to them, they kept cheering each other on. “We have to really work together here!” “Good idea!” “Why don’t we try . . ?” In this picture you can see that the pieces of paper represent both school buildings and the large grey paper represents the gravel field complete with goal posts.

P1020936Here is the same group again from a different perspective. These students had thought out breaks in the fence (for entrances, parking lot, etc.) They had included the playground, the basketball court, the concrete soccer area, the stairs to sit on and watch, the spinners, etc. etc.

Anytime somebody said, “What about. . .?” everyone stopped and figured out a way to adjust the map. This was the beauty of building this rather than trying to draw and continually erase.

This group even cut out green circles of paper to represent trees as they would look circular from above. Clever

P1020940I love this version of a parking lot spaced out using lego pieces. The problem for this group is that it was too big compared to the scale of their buildings, etc. How could they take this idea and modify it? Unfortunately we ran out of time before they could think this through. The little green triangles represent the grass on the sidewalk surrounding the school.

Why did we do this? Well, for many reasons. We are beginning a mapping unit to look at Canada in North America. I wanted students to understand that the drawing on a paper of a map is a representation of the world we actually live in. This is very hard for some students to grasp because of course we don’t inhabit a flat two dimensional world. I thought if we tried to represent our “little world” of Seymour School on a map (built, not drawn and from a bird’s eye view perspective) it might open up our thinking when we try to visualize how a map represents places we live. If nothing else, it was an awesome hands on, creative, student centred activity. Lots of thinking. Lots of discussion. A little bit of arguing (of course 🙂 ) Some new perspectives. Well done Division 5!