Nov 17
2011

MATH TALK: THE POWER OF “I WONDER”

by Christine Losq

Great teachers inspire their students to wonder; teachers who do are WONDER-ful.

Recently my friend Nan demonstrated the power of two little words, “I wonder,” for getting her fifth graders involved in critical thinking. I wish I had a video of how she does this, but in this case, words will have to be enough.
Here is the set up for the lesson. A description of how Nan uses “I wonder” to  inspire kids to think follows.

Goal: Understand the concept of variables in science
Activity: Make a simple pendulum, observe how it works, gather data to analyze
Materials: (for each pair of students) a length of string, scissors, a ruler, a large paper clip, a penny.
  • Step 1: Have partners work together to cut a length of string exactly 36 inches long.
  • Step 2: Tie a loop at each end.
  • Step 3: Set the ruler to extend over the edge of a desk.
  • Step 4: To make a pendulum, loop one end of the string on the end of the ruler.  Attach the large paper clip to the other end of the string.
  • Step 5: Slip a penny into the clip.

Experiment
Set the clip to swing and count the number of swings in 15 seconds. Record the results. Repeat several times. Then share and compare your counts with the class.

Discussion
“I wonder why we got so many different results,” Nan mused.
Hands shot up with ideas.
“What counts as a swing?”
“How far back should we pull the clip?”
“Maybe the strings are not all the same length.”
“Would it make a difference if we used two pennies?”
Students had spontaneously listed VARIABLES for which they could test on the next round.
When a teacher routinely models “I wonder. . .” the way Nan does, students are drawn into the question and invited to think more deeply. Wondering provides an easily-accessible entry point into higher level thinking.
The BEST part of modeling “I wonder” comes when your students start wondering on their own.
“I wonder what would happen if I changed this number.”
“I wonder what would happen if I rotated this hexagon.”
“I wonder why some fractions seem hard and others seem easy.”
“I wonder what the character will do next.”
“I wonder how I would feel in that situation.”

So next time you want to start a class discussion, start by wondering about something in your lesson plan.

From all of us here at MathCoach, have a WONDER-ful Winter Break.
See you again in the new year!

Grade 5 math Measurement

Mar 23
2011

Measure Length to the Nearest Fraction of an Inch

by Christine Losq

Question: Why do kids struggle to measure to the nearest fraction of an inch?
Answer: Rulers are so full of information that kids suffer information overload.

I love watching skilled teachers at work and my friend Nan is one of the best. Here is a 10-minute activity she thought up that kids loved. At the end of it, they had become ruler pros.

Objective: Have students describe a ruler so that someone who has never seen one before can draw it.
Easy set-up: Project the image of a ruler on your white board, or distribute rulers to pairs of students.
Ground rules: Students take turns giving clues. The teacher attempts to draw exactly what the students describe. Each student may give only one clue.
Managing group discussion: Have speakers hold an object like a pointer or a bean bag. Students then know whose turn it is to speak.

Here is a peek into how this activity played out in Nan’s classroom.

Nan: “I don’t know what a ruler is. Help me picture what it looks like!”
Student 1: “It is a stick with lots of little marks on it. And numbers 0 to 12.”
Nan draws a line with random tick marks and numbers all bunched together.
Student 2: “NO! Not like that. The marks are evenly spaced.”
Nan: “Tell me more. What do you mean evenly spaced? Are they all the same size? Are they all the same distance apart?”
Student 3: “OK! OK! Stop! Start over. First draw a long skinny rectangle. Then mark off numbers 0 to 12. But you have to make equal spaces.”
Nan starts a new drawing, using the new clues.
Student 4: “Yeah, like that. Now put a little mark above each number. It should be about half as wide as the rectangle. NO! I mean half as tall.”
Student 5: “Now you need to put more marks between the numbers.”
Nan: “Where should they go? Are they all the same size? How many of them do I need to draw?”

You get the idea. Nan asked clarifying questions to help her 23 students refine their clues. Students were engaged in solving the problem, used math language, visual analysis, and verbal descriptions, and gained important understandings of what the different-length ticks on a ruler show.

Here are some patterns students discovered:
1) The inch ticks on a ruler are longer than any other ticks.
2) The half-inch ticks are exactly midway between the inch ticks and are shorter than the inch ticks.
3) Other ticks are halfway between inch ticks and half-inch ticks. These are quarter-inch ticks and are shorter than the half-inch ticks.
4) There are tiny ticks halfway between the quarter-inch ticks. These are eighth-inch ticks and are the shortest.

Now students were ready for skillful ruler use to measure everyday objects to the nearest fraction of an inch.

Nan used this activity as part of her unit on fractions. Ruler skills reinforce and deepen a knowledge packet related to fractions and mixed numbers. Ruler skills help students locate fractions and mixed numbers on a number line, compare and order rational numbers, and understand the meaning of half of a half, and half of a fourth.

Try it yourself! If you’d like to share your own ideas, click here and then click Contact! Let’s all work together!

Grade 5 math Measurement