All posts by Spencer Olmsted

5th Grade Teacher, Pioneer Elementary

Division Story Problems

div-stories2

Students wrote some interesting division story problems today. We talked about making them real – though that can be tough – and we talked about making them meaningful – though that is certainly a challenge. I proposed to them that math should either be rather interesting or rather useful. Though story problems can fall into this category, they often don’t. For some senseless math check out what happens when we do stuff to numbers… because that’s what we do in math (not really). In the end they came up with a number of interesting and engaging problems that produced more to think about in their creation than in their solving. Here are a few:

There are 160 people at a party and there are 40 pies. Each pie is cut into 7 pieces. How many pieces would each person get?

Sasha made 117 cupcakes. She had platters that held 12 cupcakes each. How many platters does she need?

There are 157 students going on a field trip to Nisqually. There weren’t any buses, so they had to order “10 person” vans. One person brought their mom, dad, brother, and sister. Three teachers came as well. How many vans do they need to order?

The clock factory produces 20 clocks per hour. 143 clocks in the clock factory are finished. They are packed into creates that hold 44 clocks each. How many crates do they need? How many clocks are in the last crate? How long did it take to make the clocks in the first crate filled?

There were 260 3rd graders at a summer camp. Half of them were going to Great Wolf Lodge. A quarter of them were going swimming. The last quarter was staying at camp. The larger group took mini-buses that held 13 campers. The smaller groups took cars that held 5. How many buses and cars did they need?

I think some of these students could write for textbook companies! It’s interesting to see their worlds reflected in their math problems, and I was particularly happy to see how engaged they were in the process.

Shape Classification

image001This month we are working on classifying quadrilaterals. Creating these overlapping hierarchies is  always a challenge. Relationships that work one way, don’t work the other way, and there is a lot of specific vocabulary that needs to be learned and applied in novel situations.

It’s a little like this: everyone who lives in Olympia lives in Washington, but not everyone who lives in Washington lives in Olympia. Bringing it back to the shapes – all squares are rectangles, but not all rectangles are squares.

To do this work, we need to know the defining characteristics of the quadrilaterals that we are classifying – and here we run into yet another difficulty… mathematicians don’t always agree on these! But the work of classification goes on. We just learn the specific characteristics and create the relationships accordingly. Here is a table that tries to communicate these overlapping relationships.

quads-3Under the inclusive definition of trapezoids, all six shapes a the top of this post are trapezoids, under the exclusive definition only three of them are… can you spot them?

Ninety-Ten

90-10We were playing this game in math class today called “I have, You need” during which the number ninety-ten came to my attention.

The game is pretty simple – one person thinks of a number between 1 and 99 and the other person comes up with the number that will add to that number to make 100. Warming up we start with numbers like 30, 45, 75 etc. Then we move on to more difficult numbers like 37. Many students will think first that 73 is the matching pair. This is because they want to make 100 and they know that 30 and 70 go together. When I explained ninety-ten, the problem became much easier. They were now trying to make nine tens, so 63 was immediately identified.

Sometimes we need to think about numbers a little differently. From place value to working from left to right, there is much more freedom in math than we’ve been led to believe. Create something new!

101qs

955-san-francisco-house

What’s the first question that comes to your mind?

Dan Meyer, prolific blogger, high school math teacher, and current Ph.D. student at Stanford wants to know. Dan has decided that there are way too many artificial scenarios in his high school math texts that pretend to model the world. He wants to see the real world in his math class because he sees the math in the real world.

101qs.com is the brainchild of Dan Meyer. On this site, anyone can post an image or a short video and let the world ask the math questions that naturally arise from the scene.

From this, he and many of his followers have created lessons where the students can generate the questions (probably the ones that the teacher has in mind), ask for any relevant information they need, and solve real problems the way they would in the real world.

It’s fantastic – check it out, but don’t be surprised if you find yourself seeing math problems everywhere.

How about this one?66-the-ticket-roll

How many do you think there are? What number is just too many? What number is too few? Be brave.

What do you need to know?

YouCubed (and more on fluency)

youcubed-thumbJo Boaler, a math education researcher and professor at Stanford University, launched a new website this past year (YouCubed) to help teachers, students, and parents navigate math education. She recently published a short paper on math fluency. In it she discusses the problems with associating math fluency with speed or memorization.

Interestingly, the Common Core intends this de-emphasis on speed but the word “fluency” is often misunderstood by textbook publishers. The newly adopted Bridges Curriculum seems not fall into this category – their strategy for building fluency is based strongly on number sense. (Read an excerpt from Jo’s paper below)

This past September the Conservative education minister for England, a man with no education experience, insisted that all students in England memorize all their times tables up to 12 x 12 by the age of 9. This requirement has now been placed into the UK’s mathematics curriculum and will result, I predict, in rising levels of math anxiety and students turning away from mathematics in record numbers. The US is moving in the opposite direction, as the new Common Core State Standards (CCSS) de-emphasize the rote memorization of math facts. Unfortunately misinterpretations of the meaning of the word ‘fluency’ in the CCSS are commonplace and publishers continue to emphasize rote memorization, encouraging the persistence of damaging classroom practices across the United States.