Archive for the ‘Math’ category

Greater Than, Less Than, Equal to

May 13th, 2009

Here is a lesson written for first graders that teaches the concept of the greater than, less than, and equal to concepts. The lesson makes use of two Gators and a Clam. It is a fun way to help students grasp the skill of using those tricky symbols!

>, <, = Lesson Plan

Subject: Math Grade: First Grade

Lesson/Topic: >, <, and = Length: 50 minutes

Unit: Greater Than, Less Than, and Equal to

Objectives:

Students will be able to compare two quantities (up to 12) and determine which is greatest and least amounts.

Students will be able to compare two quantities (up to 12) and determine when they are equal.

Students will use the symbols >, <, and = to show a true equation between two quantities.

MA Standards:

2.N.1 Name and write (in numerals) whole numbers to 1000 and order the numbers.

2.N.2 Identify and distinguish among multiple uses of numbers, including cardinal (to tell
how many).

2.N.4 Compare whole numbers using terms and symbols, e.g., less than, equal to, greater than
(<, =, >).

Materials and Resources:

Each of the teacher made items will be used to provide instruction at the beginning of the lesson.

1 Greedy Greater Than Gator (Teacher made)

1 Lester Less Than Gator (Teacher made)

1 Pond Place mat (Teacher made)

Each child made their own Greedy Gator and Lester Gator in the previous lesson. The pond place mats are laminated so the children can write the quantity of  food in each pond directly under each island.

1 Greedy Greater Than Gator (1 per child)

1 Lester Less Than Gator (1 per child)

1 Pond Placemat (1 per child)

1 >, <, = Worksheet (1 per child)

1 Dry Erase Marker (1 per child)

1 Bag of Beans or other counting manipulative (1 per child)

1 number line per child (optional)

Introduction:

Students should gather on the “carpet area”. State the objectives by telling them that at the end of today’s math lesson, you want them to be able to say, “I learned how to compare two numbers and use symbols to tell if they were greater than, less than, or equal to one another.”. Ask them to recall the math lesson from the previous day. Review concepts taught: place the “Greedy Greater Than Gator” and the “Lester Less Than Gator” on the whiteboard (they’re magnetic). Ask for a volunteer to briefly recall the story about Greedy and Lester. They should remember which is which-Greedy and Lester have to share the pond, but both agreed that they will ONLY eat from their own island in the pond. And even though Greedy always wants more, he is honest. Review the names of each symbol (gator’s mouths) and how they are read. Also, that the open mouth always points to the larger number. In the case of the “lesser than” symbol, the smaller end of the symbol points to the smaller number. On the place mat, show the students that there are 6 pieces of food on the first island and 4 pieces of food on the second island (draw big round dots to represent food). Have the students tell you how many are on each side as you draw them and then write the number underneath each island.  Ask for a show of hands for a volunteer who can show how to make the equation true using one of the gators. Have the students read the equation with you. Next, switch the numbers. Call on a volunteer to demonstrate. Again, have the students read it with you. Review how we know which sign is which. Next, ask the students which sign we should use if 2 pieces of food were added to the first island(add the food). Ask the students how many pieces of food there are and change the number to show 6 on each side. Tell the students that because both sides are equal (write the word on the board) we use a different symbol. Show the kids that neither gator works because not one side is lesser or greater than the other. Tell the kids that our equals sign is the same sign we use when we are answering addition and subtraction facts. The equals sign tells us that the equation is true. Introduce “Eli the Equals Clam”. Tell the students that when two numbers are the same, they are equal. And during our activity, we will use Eli the Equals Clam instead of the gators to show when two numbers are the same. Use Eli to show the following examples on the board:

1. 5=6 Ask the students if the equation is correct. Demonstrate how to make it true and explain why. Call on students for ideas.

Repeat with:

2. 3=4

3. 7>9

Procedure:

Tell the students that they are going to work with their gators as well as the “equals clam” to show true equations. Remind students that the open part of the gator always points to the bigger number and when the numbers are the same that means they are equal. Show students a copy of the practice worksheet. Instruct students on how they will complete the worksheet and show their work using their gators, clam, and a place mat. The first one is done for them. Ask students to recall how they used their gators and mats for the previous lesson. For example #1 reads:

1. 1 > 0

The children should write the 1 under the first island and the 0 under the second. Next, they should show 1 bean on the first island and none on the second. In the space between each island, they should place a gator or a clam to make the equation true. The students should then write the correct symbol on their worksheet for that same equation. Encourage students to refer to the number lines on their desks if they are unsure of the value of each number.

As students work, ask them questions to encourage their thinking. Some questions are:

1. What happens if one island has none?

2. How do we read the equation when both sides are the same?

3. If this group has the least amount, how much does the other have?

4. Why are you placing your gator in that direction?

5. What are the gator mouths used for?

Allow students approximately 30 minutes to complete the independent activity.

Conclusion:

Direct students to join on the carpet area. Ask the students to share some of the things they learned in this activity. Ask the students: When did you use the equals clam? When did you use the greater than gator? the lesser than gator? Did you think this was hard or did you feel comfortable using each animal/symbol? Do you think you could use the gator mouths/symbols without the gator bodies? Tell the students that will be the focus of our next lesson! Have the students recall what the objective is by repeating it. Ask them if they feel that is what they learned today. Hopefully all of them say yes! Have the children turn to the person next to them and tell what they learned in math today.

Assessments:

Students will be informally assessed throughout the lesson. They will be assessed on their participation in the group discussion and individual activity as well as on their completion of the in-class worksheet. Observations of how students show each equation on their work mats and questioning (see above) of how they obtained their answers will also be used to determine their level of understanding.

The following rubric will be used to assess the completed worksheet: (Total number of questions=15)

4=All correct    3=10-15 correct    2=5-10 correct    1=5 or less correct

Extensions:

Have students compare numbers greater than 12.

Have students write two numbers and compare without using manipulatives.

Have students compare two numbers and then tell them to add or subtract from one side to demonstrate an inequality (example: “Show me 5<8. Now add 4 to the first island. How is the equation read?”).

Modifications:

To challenge-for students who can easily identify which groups of numbers are more and less, the student(s) should be given gators that have been cut to expose only the mouths (the symbols). Students should then compare the quantities using just the symbols.

To simplify-for students who are having difficulty identifying which groups are more and less, the student(s) should be told to count each “piece of food” aloud and to place a picture of the matching number with the manipulatives for each island. The student(s) should then do the same for the other island. Using a number line, have the student(s) determine which number is more than the other. Demonstrate how “Greedy Greater Than Gator” will eat the number that is on his island-this number comes first and it is more so we read the symbol as greater than. Repeat the process to develop understanding and independence.

You can also have struggling students who may need help work with a buddy. That way you can monitor them more closely and provide help.

Another strategy would be to fold the worksheet in half and have a student complete only part of it if it is too difficult or overwhelming.

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What is Symmetry?

April 7th, 2009

The lesson will begin with the students seated at their desks. The students will be shown a picture of a butterfly. The students will be asked what it means to say that the butterfly is symmetrical. Students may recognize that one side of the butterfly is the same as the other. Students will be told what symmetry means and told that many things in nature often have symmetry/are symmetrical. They will then be shown several examples (a leaf, a rainbow, a daisy,etc.  They will then be asked if they can name anything in the classroom that has symmetry.  Examples will be given. The students will then be introduced to the activity. Each student will receive a copy of dot paper. Once distributed, the class will be shown how to fold the paper in half lengthwise along the center line. With the paper folded in half, I will use an overhead projector to demonstrate how to cut out a triangle, leaving the uncut fold as one side. Students will be asked to do the same. Before children unfold their papers, the students will be asked if someone can draw a picture on the chalkboard of how he or she thinks the figure will look once the paper is unfolded. The children will then be asked to unfold their papers to see what figure was created. Students will be asked to tell how the halves on both sides of the fold are alike. Some students may recognize that both halves show triangles that have exactly the same shape and the same size. The students will then be told that when the halves on both sides of a line match in shape and size, we can say that figure is symmetrical and we can call that line a line of symmetry. The students will then be given a picture of a heart cutout. Students will be asked to draw a line of symmetry on the heart. Students should recognize where the line of symmetry is. Students will then be given construction paper in order to make other shapes-a square, a circle, or an invented one. How to fold and cut the paper will be demonstrated. For each shape,  students will be asked to draw the line of symmetry on it.

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Birthday Sort

March 15th, 2009

Abstract:

This lesson is an interactive way to teach students how and why graphs are used. This lesson is fun for the kids and they get to learn about their classmates birthdays.


Mathematics
Kindergarten
Students will sort themselves according to birth date. Students will graph the number of birthdays within each month and determine what information the graph provides (e.g. which month has the most, which has the least, and which (if any) has the same number of birthdays).
IMPLEMENTATION
Students have already been introduced to sorting and graphing. A lesson on sorting students according to hair color, eye color, and gender precedes this lesson.
Students will gather and sit on the carpet area. Students will be asked if they know when their birthday is. They will then be asked if they think they share the same birthday with someone else in the classroom. They will then be asked if they think they share the same month as someone else in the classroom. As a group, we will briefly discuss that it is more likely that two people will share the same birth month rather than an actual birthday. The students will then be given instructions for the acitivity. Students will write their first names on a strip of paper. Large cards will be placed on the floor in the classroom. Each card will have the name of a month (pictures could also be added to help students identify the months-ex. a clover for March). The students will be directed to find the card with the name of the month they were born in and form a line behind it. Once the students have found their particular birth month, the students will be directed to count the number of students in the line they are in. The students will then be directed to look at the number of people in other months. On the dry-erase board at the front of the classroom, a graph will be present. The “x” axis will have numbers 1-10 and the “y” axis will have the name of each month in order from January to December. Once prompted, each group will be called up to the board. With teacher assistance, each student will place their name (written on a strip of paper) in the column of their month. Once completed, the students will be asked what the graph tells us. The students should be able to recognize that the graph reveals which month(s) has the most bithdays, which month(s) has the least number of birthdays, and which months have the same number of birthdays (if any). As a group, we will check our answers by counting the number of names for each month to accurately determine which month has the most, the least or the same number of birthdays. Students will then be directed to ask members in their month to determine if any share the same birthdate. In closing, students will be asked to share what they learned about using a graph.
Students will work collaboratively & individually.
1 class period. 30 Min. per class.
MATERIALS AND RESOURCES
  • Materials and resources:
    Twelve large cards with the names of the months and dry-erase/chalkboard
Strips of paper
STANDARDS & ASSESSMENT
• Subject : Mathematics
• Subject/ Grade/ Domain : KINDERGARTEN
Data Analysis, Probability, and Discrete Mathematics
Every student should understand and use all concepts and skills from the previous grade levels. The standards are designed so that new learning builds on preceding skills and are needed to learn new skills. Communication, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of mathematical strands.
Data Analysis (Statistics)
Understand and apply data collection, organization and representation to analyze and sort data.
Formulate questions based on data displayed in graphs, charts, and tables.
Students will be assessed acording to their participation, understanding of what is taking place, and their ability to follow directions throughout the group activity.
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