I knew that if the students thought of the problem as “one-half of one-half,” they would agree with the answer of one-fourth. Then give them practice applying it to other fractions. This question has one right answer (the least common multiple for the numbers 4 and 6 is 12),but students may arrive at the answer in different ways. As we collect data for other situations, we’ll look to see how the mean, median, and mode compare. Four times one equals four. Underneath Kenny’s equation, I wrote: I said, “I think that my open sentence is the same as Kenny’s in one way and different in another way. 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.”. Finally, have the student who suggested the numbers describe any differences that the class didn’t find. Brian’s paper was easier for me to understand, mostly I think because I had reasoned through Laura’s paper first. “It’s two and five hundred sixty-two something,” he said. When I put them in two equal stacks, there is one penny left over. The sum of those factors is Partner B’s score for that round. And the same thing happened in the two other stores.”, Gissele said, “I tried twenty dollars, and that was even worse.”, Gissele giggled. I explained the problem we were working on and invited them to try to solve the problem with us, which produced a few looks of panic in their eyes. What do you know about shapes? “I know, you count by fives and color one of those sections in each time until you get to thirty. I then wrote on the board: Remainder of 1. The state flower is the sunflower. After Rafael heard the other student’s reasoning, he replied, “OK, I see what you mean.” Along with illustrating and labeling many geometric shapes and concepts, Rafael drew tools that he associated with geometry. Students apply all the concepts in an activity that involves enlarging a picture to scale so that it fits on a piece of graph paper. “It’s like three times sixteen is forty-eight,” Jason added. Conduct a whole-class discussion to discuss certain methods. I recorded my turn on my side of the chart. 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.”. Using different-colored square tiles or by coloring on squared paper, represent square numbers as squares to help students see that they can be represented as the sum of odd numbers. She said, pointing, “From the top to the bottom it goes 1, then 2, then 3, then 4, then 5, and so on, up to 8.”. I drew a number line on the board to help the students keep track of their guesses. 2. I wrote 95 under the Start Number column. “Come up and show us,” Danielle urged. How many groups would there be?” Some hands shot up immediately. So, for this problem, I think about a rectangle that is one by one,” I said. I want you to practice by brainstorming some possible clues for the number ten.”. “What do you notice about the shapes of the tables?” Cheryl then asked. That’s not likely,” Steve said. Sometimes I focus on their writing errors; other times I keep the focus just on the mathematics. Amanda walked up to the board and wrote: “When you put zero beside these numbers, it makes them bigger,” she said. To begin, I projected an overhead transparency of the inch-squared paper, which was a 9-by-7 grid. Katia nodded. How does your total height compare to the height from your feet to your navel? The Golden Ratio is the ratio of a person’s total height to height from their feet to their navel. “Aziza’s riddle helped us think about number riddles,” Danielle said. When you have four digits after the decimal point, the number refers to ten thousandths.”, Isaac asked, “So what’s the answer? I removed the 5-by-8-inch index card, folded it in half the short way, and cut on the fold. At the end of the second 2.561, she added a 2. Teachers Teaching Tools Homepage. The teacher could think about pairs of students who will work well together during this unit and identify subsets of students that she wants to bring together for some focused instruction. Students may need to make a list of integer addition problems whose sums are negative and look for commonalities among them in order to answer this question. Lupe made an error when she divided 40 by 11. Giving the students some visual tools is essential. Partners measure, record, and…, Vocabulary instruction is a large part of geometry instruction throughout the elementary grades. “Did any tables find any other factors of two?” I asked. You need to enable JavaScript to run this app. I’ll tell you the number is somewhere between one and one hundred.”. Teaching Arithmetic: Lessons for Decimals and Percents, Grades 5–6 After students shared their answers and the methods they used, I gave them other problems to solve, using other amounts for the sizes of the large and small bags. No one else had a question and the students went back to their desks to work. Write the words you made underneath the pasta letters. The author must be guessing.”. He noted that in his third grader Lisa’s response (see Response. Elise piped in, “And for the last clue, zero keeps all things the same when you add zero to it, like zero plus one is one or zero plus ten is ten.”. The language of prime and composite had not yet been introduced, but the children quickly learned that they needed to stay away from prime numbers after that first move because they could not earn any points on the resulting move. Daniel nodded “yes.”, “I know another way,” Eli said. I explained the rules, “To play this decimal game, you first clear the calculator so that the display reads zero. I want everyone to have some time to think. Focus on the problem of too much pizza. And then divide 90 by 4. “Yes,” I replied. I crossed off 30 and posted it on their side of the T-chart while keeping a running total. I wrote the words intersecting line segments underneath my sketch on the whiteboard. When Kenzie and I added ours up, it was only eighty-eight. What is one-half of one-half?”, I heard several answers. “It has clues that help you solve it,” Ramon added. Math and Nonfiction, Grades 3–5 Hold it so all students can see it. Many chose a paragraph from a book they were presently reading. The lesson gives the children experience recording, organizing, and…, A
 Lesson 
for 
Kindergartners by 
Chris 
Confer In 
this 
lesson, 
excerpted
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 Chris
 Confer’s 
new 
book
 Teaching
 Number 
Sense,
Kindergarten
 (Math
 Solutions
 Publications,
 2005),
 children 
learn 
that 
numbers 
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 purposes. When Cheryl finished reading the story, she asked the class, “What was Mrs. “Well,” I told the class, “you’re right. It turns out that f(x) f0(x) is a degree ve polynomial whose x5, x4, x1, x0 coe cients are respectively 3, 10, 25, 12. In the same way, ‘n over d’ is a general name that could mean any fraction, but ‘six-twelfths’ refers to a specific fraction because you now know what numbers you’re thinking of for the numerator and denominator.”. ), Cheryl also arranged the tiles in a way that didn’t follow her rule and had students explain why. that’s 80 slices . So the perimeter of the 2-by-2 rectangle is 8 units.”. That equals two hundred fifty. In seven weeks, we collected 250,000 pennies, and we plan to continue at least until the end of the year to see how close we get to 1,000,000. “I’m not sure. I hadn’t thought about zero as an answer,” Danielle exclaimed. Get help on the web or with our math app. “Does anyone know what we call four in this situation?” I asked the class. Maryann Wickett created this simple yet powerful fractions lesson and then built on it, doing an activity from Marilyn Burns’s Teaching Arithmetic: Lessons for Introducing Fractions, Grades 4–5 (Math Solutions Publications, 2001). “Yes,” Cheryl replied, “but keep your own record.”, There were no more questions. Then you place the bottom line of the angle on the line of the protractor. Good questions can set the stage for meaningful classroom discussion and learning. I’m impressed with everyone’s thinking. It involves understanding and applying various relationships, properties, and procedures associated with number concepts (Math Matters, Chapin and Johnson 2006). incomplete or inaccurate. “Well, he was in the hole with eight dollars but not with nine dollars, so maybe it’s in between,” Alexandra said thoughtfully. From Online Newsletter Issue Number 7, Fall 2002, Related Publication: She went to school and invited six, but friends who were not invited begged to be included. After all of the students had posted their initials, we counted the Post-it Notes to verify that there were twenty-five of them. I then told the students what they were to do next. Hernan nodded to show his agreement. I was glad she had made the multiplication connection, but I needed to prompt her a bit to get her back on track. Over the years since I wrote the original unit, I’ve learned a good deal more about teaching multiplication to third graders from…, This excerpt is from the introductory lesson in Maryann Wickett, Susan Ohanian, and Marilyn Burns’s book, Teaching Arithmetic: Lessons for Introducing Division, Grades 3–4 (Math Solutions Publications, 2002). So it works.” I wrote on the board: Anita said, “We split the six into four and two. 12/15 is bigger than 12/16 so 4/5 is bigger than 6/8. There’s something in this diverse collection for everyone, which is sure to add an extra bit of oomph to your math instruction. Continue the process of pairing up with partners having a different number of cubes, combining the cubes, and then splitting them into equal or near equal stacks. Betty went to the local fabric store for fabric to make curtains. Now watch as I draw a rectangle inside this one with sides that each measure one-half.” I divided the square, shaded in the part we didn’t need to consider to show the 1/2-by-1/2 portion in the upper left corner, and labeled each side 1/2. Jeffrey raised his hand. Figure 1. “Oh,” Kathleen responded and then began to build a rectangle that was four squares wide. “Each of these is ten percent.”, Sam chimed in, “Just cut them in half, and then each will be five percent.”, I colored one twentieth in and labeled it five percent. Nicole answered first, “There wasn’t going to be enough room, because when you push tables together you lose chairs,” she said. We then figured out that 36 percent lived at three-digit addresses and 20 percent disliked He wrote: This notation for division isn’t standard to algebraic representation, which I wanted Donald and the others to know. 1.Player A chooses a number on the game board and circles it. Once Ben had recorded my turn on his chart, I handed him the die, indicating it was his turn. How is multiplying the dimensions to find the volume similar to using the layers approach? “What about twenty-five hundred?” I asked. ... Am I the problem, or part of the solution ? I decided to move on rather than continue to discuss this point. by Stephanie Sheffield and Kathleen Gallagher, From Online Newsletter Issue Number 16, Winter 2004–2005. Randy also solved the problem by drawing a picture. Skylar told me his start number was ninety-five, and the class agreed. Some students remembered that a square was a rectangle, but others didn’t. But that doesn’t make sense, because 16 times 2 is 32. Another Innovation.. Music Logos is the crowning piece gives instant answers to Music Theory. They
 search 
for
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in
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school, 
draw
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 of
 things 
that 
have 
numbers, discuss 
how 
numbers 
help
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 well
 as
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to
 adults
 in…, A Lesson for Kindergartners and First and Second Graders by Linda Dacey and Rebeka Eston The collection and display of data are important to our lives, and through their own investigations, young children begin to understand how they can find and communicate information in data, charts, and graphs. I showed them the worksheet of grids and said, “I’m going to give each of you one of these. The general consensus was that guessing and checking, working backward, acting it out, and looking for a pattern were the most used problem-solving strategies.