# Math Unit Lesson Plan BREN by keralaguest

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Seven Peas and Carrots

Bren McGuire
September 28, 2004
Math – Number Sense and Multiple Representations

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
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.
 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.
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
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.

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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