by folding a square of paper in several predetermined ways, children investigate and record the different shapes they can make. students are taught various sentence frames and use the… 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. each page shows what is above and below the water of a young girl’s backyard pond. the book provides engaging, quick activities to help students practice math concepts, skills, and processes in a variety of problem-solving contexts throughout the day. to learn geometric terms and their meanings, students need opportunities to interact with and use the language of geometry. i was searching for ways to teach arithmetic with the same excitement i had for the other areas of the math curriculum. the learning model asks students to first develop their… a lesson with second graders by linda dacey and rebeka eston salemi all teachers have students with a range of mathematical abilities and understandings in their classrooms. to prepare for the lesson, i duplicated for each pair of students the shapes for the activity and a sheet of inch-squared paper. (when the students later worked on finding the areas of shapes, i nagged them regularly to identify the units and record them in one of these ways.) i suggested to some students that they place a shape on the inch-squared paper and count the squares it covered. then, whisper your ideas about the answer to a partner.” danielle first gave students time to think and take notes. first, you have to think of a number to write about. i want you to practice by brainstorming some possible clues for the number ten.” danielle gave the students about five minutes to work in groups. 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. this question aims to help students generalize about the relationship between the sign of the sum and the numbers in an integer addition problem. “when you play this game, each of you will need your own recording sheet,” i said as i drew two two-column charts on the board, one for me and one for ben. “i think cindy’s idea will be clearer after you’ve had the chance to watch the rest of this game and play for yourself,” i said. subtract that from three hundred and you still have three turns to get one hundred ten more points.” “look, i can win!” he said. i waited for a few moments for the students to settle down and then showed them what else to record when they played. can anyone think of a factor of two that’s not already up here?” i asked, pointing to the overhead. “see if you can think of any other factors of two.” i let the students talk briefly and then i called them back to attention. looking for patterns is a powerful way to build number sense, particularly when students have opportunities to think about the patterns and their relationships to numbers and operations. after two games, i was satisfied that the students understood the rules and knew how to determine a winner. with your partner, see if you can apply each of the methods displayed to a three-by-four-by-five-unit prism. i think there are more than twenty-three marbles because i could get about ten marbles in a handful and i know there are more than two handfuls in the jar. as i read the book, listen carefully for strategies you could use to estimate. i used twenty because that would be how many marbles were taken out of the jar for it to be one-fourth empty. 11. show students the bags of kidney beans, explaining that they’ll be working with a partner to use a strategy for estimation from the book to estimate the number of beans in their bag. in the example task below, students may limit their consideration to only a few shapes or by focusing exclusively on two-dimensional shapes. he often made diagrams to summarize the events in a story and his language often reflected his visual preference. “i’m interested in all of your ideas.” the students had a variety of ideas. i wrote the number 40 in the first basket and the number 4 in each of the other two. 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. i had deliberately picked an easy number to start with so we could focus on the mechanics and thinking involved with the game. also, i was giving them a preview of the discussion to come. playing guess my number with a 1–100 chart gives students further exposure to the chart and pushes them to articulate some of the number relationships inherent in it. then, to begin the lesson, i gathered the students on the rug and showed them the journal. soon i interrupted the students for a whole-class discussion. “you have to add ten to the five and then divide by two. i called the class back to the rug for a concluding conversation, and the interchange was lively. in the story, mr. and mrs. comfort invite 32 family members and friends for a reunion and set eight square tables to seat four people at each, one to a side. when everyone had had a chance to work on the problem, she interrupted the students and asked for their attention. be sure to record the dimensions of each table and the number of people it will seat.” she watched kathleen make a 16-by-2 rectangle. by the end of the period, she saw that all of the students had found some of the rectangles and some had found them all. “can i show it?” cheryl nodded, and anfernee came to the board. here, fifth graders explore just one of the predictions made in the book and use estimation, multiplication, and division to make a prediction of their own. there is more to this book than could possibly be read in one sitting, so i read just enough to give the students the flavor of each section. figure 1. cameron and mason clearly understood how to calculate the number of times they could blink in three minutes, three hours, and so forth. i explained, “you can use a dot in this way instead of the times sign that you usually use for multiplication.” i then asked the students to write examples of arithmetic equations that were true and some that were false. i was pleased that kenny had volunteered the use of a triangle. “yes, i used a box for the variable and kenny used a triangle for the variable,” i said, taking the opportunity to use the word variable. i began one class lesson by asking the students to think about two fractions—6/8 and 4/5.“which is larger?” i asked them. i read laura’s explanation again and realized that she had converted the fractions so that they had common numerators. also, it was easy for me to understand because her approach mirrored the way i had thought about the problem. then i wrote two fractions on the board—3/4 and 2/3—and asked each student to take out a sheet of paper and convert these to common denominators in two ways – mariah’s way and raul’s way. i wrote the list on chart paper and kept it posted in the classroom for students to refer to. then you get the arrow and take it up to the number and the number that the line hits is the degree of your angle. to make angles you use the bottom part of the protractor (shown on pages 3 and 4) to make any angle you disire.
decide if there could indeed be measurements between two and five-tenths pounds and three pounds and, if so, discuss the possible weights of the lobster.” the students began to discuss in pairs. we read the number aloud, and then i asked the students for solutions to the question about the in-between weights. then i asked maryann to go up to the board and place hers on the venn diagram. however, i wanted the students to reason mentally and talk about their thinking. i began the lesson by posting the chart of “true” statements about multiplying whole numbers that i had previously generated with the class: i planned to use these statements as a base for helping the students think about multiplying fractions. the students nodded their agreement, and i wrote ok next to the first statement. “one-half of six is three, so one-half times six is three, and that’s the same as six times one-half.” after a few moments, i called on brendan. i posed a problem that had a fraction as one of the factors for which the answer was greater than both of the factors. while the question was trivial for most students, i planned to build on their understanding and have a class discussion about different ways to determine that a fraction is equivalent to one-half. “and four is the bottom number, so it’s the denominator.” the idea of algebraic variables was new for these students and i tried to explain. because i’m the first player, i start with one hundred and i have to choose a divisor from the numbers listed from one to twenty. one hundred minus ninety-five is five and that five would be left over.” “i like zoe’s idea of using nineteen as the divisor,” i said. i get a score of six.” the students seemed to understand how to play and i wanted to give them fi rsthand experience with the game, so i said, “the game ends when the start number is zero, but skylar and i are going to stop here so that you can play. 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. i waited a bit more and then said, “try to think of ways that don’t use one straight cut but that still cut the brownie into two pieces that are the same size. i wanted the students to think about counting and combining halves of squares. then i wrote n over sixty is the same as thirty over one hundred to see what thirty percent of the whole number would be. i didn’t have to figure out the whole number, i just know that i colored in six blocks and each one is worth three. i crossed off 30 and posted it on their side of the t-chart while keeping a running total. 6. as we played one or two more rounds, i began to share a few of the rules—the first being that when you choose a number, the other player must be able to earn points. good questions questions such as those that follow can help to scaffold and articulate new understandings that have come about as a result of playing the factor game. for this lesson, i planned to have the students work individually to solve a measurement problem involving fractions. x 30. i think this is a good way of doing this because all you have to do is multiply the numbers and you have your answer. what i had done was put the students in a testing situation, not a learning situation. group 1 wrote: the total inches are 22.5. we think its 22.5 because each cube is of an inch and their is 30 cubes so you split one each into 4 parts and you times 30 cubes by 3. and you get 90. and then divide 90 by 4. they showed how they did the calculation. 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. the next day, i asked the students to write a word problem to match one of two equations: 1 3/4 ÷ 1/2 = ? the students understood that they needed to add 7 3/8 to 1/16, and they correctly did that, understanding that one kit needed exactly 7 7/16 inches of wood. i asked the class, “if a single serving of french fries has forty fries, how many friends would one thousand french fries feed?” i gave them a few minutes to think and then asked for their ideas. i explained to the students what they were to do. when i taught this lesson to a class in the year 2000, students reported several different methods of figuring that the penny was twenty-two years old. “the arrows mean that the line goes on forever, or infinitely, in both directions and in a straight path,” i said. i wrote the word intersect on the whiteboard and pointed to where dana’s lines intersected. to model recording, i quickly sketched a geoboard on the whiteboard and drew on it the two line segments i had made. but it’s more, so two-thirds has to be more.” one day, i chose one and one-quarter for the fraction. also, sometimes students think in ways i hadn’t thought of, giving me new ways to look at the mathematics. let students know that mathematicians sometimes use the median in a set of data to solve problems. let students know that they just went through a process of evenly distributing cubes in the group to represent evenly distributing slices of pizza. 12. call students together for a class discussion of their solutions to the problem. when you find a way to make the number one, i’ll cross off the one on the board and we’ll move on to the next number, two. the students took a minute to consider the possibilities. she asks students to get out their math journals and pencils and gather in the meeting area. dewayne refers to the value of the numbers and melissa is willing to verbalize another possibility. she secures their agreement as she points to each number in the list and says, for example, “is this a multiple of four?” two students use arithmetic to find a number that is different. then the teacher must think about product—how her students can demonstrate their ability to use and apply their knowledge of number theory at the end of the unit. i began the lesson with a read-aloud of martha blah blah. i asked the children to write two summary statements on their sheet of newsprint. i then gave the following directions: interest remained high for weeks, as students looked again and again at their classmates’ work. during what is dubbed “the storm of the century,” the wind chill is between –50° and –80° fahrenheit in duluth, minnesota. carl gorman, a gentle navajo artist and one of the 400 navajo code talkers during world war ii, dies. “ben bear says that he could sell 10 pizzas a day and that’s 80 slices,” i said, writing the numbers 10 and 80 on the board. i gave the students a few seconds to think, then called on jesus. i pointed at the fraction i had written on the board and said, “you’re trying to think of a fraction with a numerator larger than three and a denominator larger than four. i asked, “who knows a fraction that follows the rule and also belongs in this column?” i waited until about half the students had raised their hands. i explained to the students what they were to do. i labeled the first column circle number and then asked what a diameter of a circle was. a large number of students raised their hands, and nelson briefly summarized the book. (see a sample in… i began by introducing the class to one version of the game race to one.
our lessons contain an overview, vocab words, suggested procedure and activities, as well as potential follow up assignments to reinforce student’s learning. in this lesson students learn to identify and say 5 different objects in the classroom. students practice naming things in their classroom, play fun games these robust, ready-to-use classroom lessons offer breadth and depth, spanning essential social justice topics and reinforcing critical social emotional, .
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