NOVEL THINKING

Then it’s more than one, so you’re sure it works.”, “I rolled four-fifths,” Lily said. Provide background information about the author and the story. Tom added, “I know that 100 percent of the people would be twenty-five, so ten people, or 40 percent, are not in the circle.

Then I asked them to make a different estimate. By introducing several ways to think about factors, I hoped to explain the game more quickly.

“I think they’re both right. “They both have eight squares in them,” Andrew said, dividing the grid into squares to show what he meant. Amy wondered aloud if they thought it would take more or less than three rolls when they played next time. Once we agreed on what they were being asked to do, the children set off to collect and represent their data. Her colleague Jane Crawford gave her the idea of presenting older students with the problem of figuring out the ages of coins. He rolled a 5. The problems they solved included the following: 2 2/3 ÷ 1/3 = ? “On a measuring cup, the line for two-thirds is above the one-half line,” Ramon said.

Here is just a sampling of the problems they wrote: Tom was buying wood for his woodshop class. two and five hundred sixty-two–thousandths. What can this process tell us about the approximate number of slices of pizza we’d need for each person in our class? Finally, have the student who suggested the numbers describe any differences that the class didn’t find. Carol used partial products to solve 52 x 24. While Amy was expecting a simpler solution, she wrote Marcello’s idea as an equation on the board next to the 1. by Maryann Wickett and Marilyn Burns. I then wrote on the board: “What about this equation?” I asked. “We have one statement left,” I said, pointing to it: 6. I’ll say four-eighths.” I recorded this on the board. Giving the students some visual tools is essential. Then we multiplied 1½ by 15 because we used 2 cubes to make 1½ we cut 30 in half which = 15.

In this lesson, which appears in Chris Confer’s new book Teaching Number Sense, Grade 1…, Before taking my class for a leaf-collecting walk, I distributed 9-by-12-inch drawing paper and asked the children each to draw a picture of a tree.

I multiplied by four because there are four-fourths in the whole jar. She wants all of her students to be able to represent and connect number theory ideas. The others nodded, but I’m not sure they all understood that there are two ways to think about division—sharing (or partitioning) and grouping. She also knew that additional practice allows children to continually think about numbers from one to ten and provides a glimpse of the problem- solving strategies children rely upon…, by Jamee Petersen Understanding the concept of scale is not easy for young children, but Steve Jenkins’s book Big and Little (Houghton Mifflin, 1996) can help. pizza that they eat and use that information to learn about some new math ideas and to solve Moira’s problem. “Can I show it?” Cheryl nodded, and Anfernee came to the board. This book presents five completely new whole-class lessons plus five new lessons in the Additional Activities section.

I hoped that in subsequent games students would pay more attention to patterns in general as they played. That shows you used a lot of good mathematical thinking.”. They create posters to show their findings and participate in whole-class discussions to share their thinking. I called on Josh. “And they touch nine pegs, just like your other examples,” Charles added. I got eighteen also.”, Charlotte said, “If three is five percent of a number then six must be ten percent of the number and if six is ten percent, then three times six, or eighteen, is thirty percent of the number.”.

The class quickly caught on to what Cheryl was doing.

You can use scratch paper to jot down your thoughts. “I don’t get why n is three and d is four,” Gena said. As the students got to work, I heard them using correct math terminology (perpendicular, parallel, intersecting) to identify their pairs of line segments; they seemed excited and challenged by the task of finding as many different arrangements as possible. ), Figure 2. Word problems getting you down? How much did he start with? If there’s a strategy that I want students to know about and no one presents it, then I present and provide practice with it. I turned to the board, explaining as I wrote. We’ll keep that question in mind as we continue working with data and finding the median and mode. I had pairs work together to create summary statements but asked them to individually complete the writing prompts before discussing and comparing their opinions and answers. Figure 1.

(I suggest that you do this, too.) Nancy is a classroom teacher with almost thirty years of experience as well as a Math Solutions instructor. I showed them the worksheet of grids and said, “I’m going to give each of you one of these. I began the lesson with a read-aloud of Martha Blah Blah.

I said, “When I call on you, read one of your mathematical sentences. The class cheered and Ben did a little victory dance. “See if you can think of any other factors of two.”. In my early years teaching mathematics, I taught students to compare fractions the way I had learned as an elementary student—convert the fractions so they all have common denominators. I wrote her idea on the board: Alexis explained, “If you want a remainder of one, you have to find a number that you can multiply by two and get nine.”, Alexis replied, “Because if you have a problem where you divide nine by a number and get two, then if you divide ten by the same number, you’ll have a remainder of one.”. After he solved the problem, James came to me with his usual question: “Do I have to write?”. Predictions for the Millennium (New York: Puffin, 1997) is a collection of predictions about everyday and not-so-everyday events that will take place in the next three seconds, the next three minutes, the next three hours, days, weeks . . Construct as many words as you can from your letters. “I knew that ten times eight is eighty,” he explained. Ben looked delighted. “Do you think people really cut down exactly ninety-three trees every three seconds?” I asked. Figure 2: As Libby’s paper shows, the game can provide experience with fractions greater than 1.

This question aims to help students generalize about the relationship between the sign of the sum and the numbers in an integer addition problem. Visit www.mathsolutions.com…, A Lesson for First and Second Graders  By Jamee Petersen Miriam Schlein’s More than One (New York: Greenwillow, 1996) introduces the concept that one unit can be made up of more than one thing.

How could we find out. You can guess a number and I’ll tell you if my secret number is greater than or less than your guess.”. A balance of novelty, familiar routines, and physical activity—customized to your class and personal…, by Stephanie Sheffield Stephanie Sheffield begins this lesson in her first-grade classroom by reading aloud Ann Jonas’s book Splash!

“Suppose you have forty-eight apples and you share them among three people,” she said. But it’s more, so two-thirds has to be more.”.

Designed for use with children in Year 5 and Year 6 the lessons stimulate the development of children's mathematical thinking through carefully selected classroom tasks"-- Cover.

Then I stopped to give the homework assignment.

Satisfied that he understood what he was doing, Cheryl said, “What you’ve done makes sense to me.”. “I think the only way to make it true is to put eight in the box.” “I think you could make it work by fractions,” Chase said. Think of each as a brownie that you’ll cut so that two people would each get the same amount to eat.” I called on Daniel. We subtract 30 by 7½ which equals to 22½. Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4–5 The students nodded their agreement, and I wrote OK next to the first statement. 1. Discuss the terms prime and relatively prime and the distinction between them.

So the player with three hundred ten wins.”, “You’re right,” I said and continued, “You’ll each take six turns. I also wanted the students to see that math involves taking time to think. All of these sums, however, are square numbers.

“I’ll be interested in your reaction to whether this problem is too easy, just right, or too hard for fifth graders.”.

Keep a weather graph charting the temperature for a month. She came up to the board and explained, using Katia’s brownie. Some students might think for a minute or so before beginning to record their ideas, but most begin immediately. The children need to realize that although games can be great fun, as this one certainly is, good mathematical games also have purpose. “You could multiply six times fifty and get three hundred!” Mario said. “With three there would be a remainder of one because if you count by threes, you land on ninety-nine, and that’s one away from one hundred.”, “Nineteen,” Zoe said. Processing the game gives mathematical meaning to the activity. “Yes,” I congratulated. I’ll multiply by ten. Raul was particularly animated. I allowed a minute for silent inspection of the results. “If two-thirds was the same as one-half, then two would have to be half of three. For instance, I’d ask them to build a row of four, six times, and walk around…, In this lesson, students explore halves, looking for patterns between numerators and denominators. But animated conversation helped each student decide.

Now tell the students that you have another problem for them to solve mentally. Also, collections of grid paper with different-sized grids, measuring cups of various sizes, a few unifix cubes, and balance scales and masses provide engaging estimation tools for students. Then I split the train into tens.

“Yes, I can see how you could rotate one and it would fit exactly on the other,” I said and then asked, “Who would like to divide the last brownie into halves in another way?” I called on Maria. I chose Skylar and, as he walked to the front of the room, I wrote on the board: I explained as I pointed to what I’d written on the board, “When you play, you and your partner will make one recording sheet that looks like this. He wrote: This notation for division isn’t standard to algebraic representation, which I wanted Donald and the others to know. Then you have to write some clues. “One-thousandth,” I corrected, emphasizing the that the end. How is the approach the same as ours?

You can use one, two, or all three of the numbers rolled to make the number you need.”.

It’s eighty slices divided by ten pizzas and that makes eight slices in each pizza.” I wrote 80 ÷ 10 = 8 on the board and acknowledged that there were indeed different ways to solve the problem. I called on Cindy. Figure 1. Through the use of two colors of counters, students decompose the number twenty and use number strings…, by Lynn Sherman Lynn Sherman is a teacher candidate at York University in Toronto, Ontario, where she recently taught a geometry class based on The Greedy Triangle, by Marilyn Burns (Scholastic, 1994), to a class of second graders. Before the period began, I drew on the chalkboard a line segment that measured 22 1/2 inches. She said, “You multiply six times three and divide that by two.

Christina guessed forty-two. As guests arrive, they all have their own ideas about how to rearrange the tables so that different-size groups can sit together. I wrote on the board: “Joshua wants to know if this is an open sentence,” I said. Cheryl asked Nathan to explain what he had done.

If you can’t figure it out, you do this. “How about a four, a four, and a three?” suggested Christine. Before we think about whether they work for all prisms, let’s test them with one prism. “Not if we can’t use fractions,” Ana qualified.

Continue the pairing and splitting until everyone has the same or almost the same number of cubes. “There are lines that have two endpoints,” she said. Mia said, “Some people might not be able to divide by double digits.

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