Seven Peas and Carrots Bren McGuire September 28, 2004 Math – Number Sense and Multiple Representations First Grade Standards Math Number and Operations 1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Count with understanding and recognize “how many” in sets of objects Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers Representation 1. Create and use representations to organize, record, and communicate mathematical ideas. 2. Select, apply, and translate among mathematical representations to solve problems. Outcomes/Objectives 1. Students will understand that there is more than one way to get an answer of seven, and that the ways to get seven can be shown in many ways, so long as there is a link between the number of objects shown and the number word used to count to seven. 2. Students will Count with understanding and recognize “how many” in sets of objects Realize that combinations of peas and carrots can be made to reach a total of seven Create and use multiple representations to organize, record, and communicate mathematical ideas. Understand that there is a one-to-one link between the number of objects shown and the number word used Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers Share their solutions, and show or tell how they found their solutions Vocabulary combination, one-to-one link, representation, multiple Materials/Technology Scratch paper, pencils, chart paper, marker, orange and green crayons, orange and green cubes, orange triangles, green circles, orange and green Unifix cubes, chalkboard, chalk, created worksheet Procedure Activity will begin as whole group. Then, students will be divided into groups of four to find solutions to problem. Students will come back together as class to discuss findings. Then students will brainstorm ways to show findings. Students will be put back into groups and assigned a way to represent their answers. Teacher will hand out manipulatives to the groups that need them for representation. After short period of time, students will be brought back together, and each group will show one of their solutions according to their method of representation. While students are working in groups, teacher will roam around room to observe progress. While working as whole class, teacher will guide discussion through probing and prompting questions. ENGAGE 1. Ask students to share how they got to school this morning (i.e. ride bus, walk, ride in a car, ride bike). Teacher may want to write method and number of students on board, or possibly make a graph, where a symbol stands for each method, and one symbol stands for one student. This could be a reference for the one-to- one link discussed later in the lesson. 2. Ask students what they notice about this information. Students should notice that there are different ways that everyone got to school this morning 3. Explain to students, if they did not notice themselves, that this information shows that there is more than one way to do something. Tell them that is what we will be looking at in math today – there can be more to one answer to a problem, and that there can be more than one way to find or show the answers. EXPLORE 1. Draw circle on piece of chart paper. Tell students: I have seven things on my plate. Some of them are peas, some of them are carrots. What could I have? How many peas? How many carrots? Remember, I have seven things in all. Teacher may want to write “seven in all” at top of chart paper. 2. Call on two students for answers. Teacher can show answer by modeling answers on plate with drawing. Ask students to show thumbs up, thumbs down, or mid-way thumb sign if they agree, disagree, or are not sure. Have students count the drawn objects with teacher to see if there are seven in all. If the answers provided by the two students are different, tell students that there is more than one way to solve the problem, just like in the example about the ways they got to school that morning. 3. Divide students into groups of four to have them search for as many answers as they can find. Each group should be given a few pieces of scratch paper and some pencils to work with. Teacher will need to tell students to keep track of the answers they find. Teacher should roam room to observe progress as students work. Teacher should act as a guide, not a provider of information. EXPLAIN 1. Bring whole class back together to share solutions. Try to have each group share a solution to the problem, and explain how they found that solution. As students share ideas, teacher will record ideas in a chart on chart paper. 2. When a group presents an answer like “3 peas, 4 carrots”, tell students they have made what is called a combination. They used both peas and carrots in a combination to make seven. 3. After the students have presented all solutions, teacher will have students look at chart. Teacher will ask students if there was more than one answer to the problem. Students should say yes. After this, teacher will inform students that they found multiple solutions, and that multiple means more than one. EXPAND/EXTEND/APPLY 1. After the students have presented all solutions, teacher will ask how they could show these solutions. Teacher will tell students that showing a solution to the problem, like she did by drawing the peas and carrots on the plate, is called a representation. A representation is showing an answer. Teacher will also show students that, when using representations, it is important to have a one-to-one link. A one-to-one link is when the number of peas drawn is related to the number of peas you have as a number <i.e. three peas = three drawn circles>. Teacher may want to refer to graph (if made one) from beginning of lesson. 2. Students should brainstorm and offer ideas to represent the answers on the chart. Teacher will list representation ideas on board. For example: Counting on fingers (CONCRETE) Tally marks with green and orange crayons (SEMI-SYMBOLIC) Drawing peas and carrots (PICTORIAL) Manipulatives <different colored triangles and circles, different colored cubes, Unifix cubes> (CONCRETE) Word problems <3 carrots, 4 peas> (SYMBOLIC) 3. After students have listed all of their ideas, teacher will need to make sure that there are enough ideas for one to be assigned to each group. If not, teacher will need to probe the students’ thinking for more ways to represent solutions. 4. Each group will be assigned a representation method. Teacher will tell students to show as many solutions from the chart as they can with their assigned representation method in the allotted time. 5. Bring class back together. Have each group show one of the solutions with their assigned representation method. EVALUATE 1. Ask student to return to their designated seat. Give each individual student a worksheet that has a plate with eight things on it. The student will need to find as many solutions as possible for this problem. 2. Part of the worksheet will ask the student to show two of his/her solutions with a representation. The student will be able to draw or use tally marks on the worksheet on his/her own. If the student would be more comfortable, however, using manipulatives to show his/her solution, he/she should let the teacher know, so that the teacher can meet with the student to see him/her show the answer. In this case, teacher would sign off on the student’s paper. EXPAND/EXTEND/APPLY (2) 1. As a whole class, ask students to brainstorm ways that an activity like “Seven Peas and Carrots” could apply to real life. (i.e. marbles and jacks) (ABSTRACT) 2. If teacher feels students need more practice with this concept, teacher could increase the number of peas and carrots to a different number. ADAPTATIONS/MODIFICATIONS If a particular student is found to have difficulties with this lesson, it may be necessary to decrease the number of peas and carrots on the plate, so that he/she will have less solutions to find and less to count. As student gains confidence, increase the number. REFERENCES. Kliman, M., Russell, S.J., Wright, T., & Mokros, J. (1998). Mathematical thinking at grade one. White Plains, New York: Dale Seymour Publications. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc. REFLECTION I think this is a great lesson. However, I do believe it needs to be stretched out over a period of two to three days. Introducing multiple solutions, representations, and one-to- one correspondence is too much for students at this age to grasp in one day. I will need to be aware of the achievement levels of my students, as well, so that each group is a mix of high and low achieving students. I can accomplish this by assigning the groups on a piece of paper before the lesson. However, as the students break into groups, I will need to make sure that the high achieving students are not doing all of the work and leaving the low achieving students behind in the dust. IDEAS FOR INTEGRATION I could integrate science into this activity by telling students that we have been asked to plant some flowers and ferns in a pot outside the school. In the pot, we have enough space for twelve plants, and we need to decide what combinations of flowers and ferns we could use to completely fill the pot. This conversation could then break off into what the flowers and ferns need to survive, what would happen if we planted more than twelve flowers and ferns in the space, and other ideas related to plant life.
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