Student Publications
Author: Hanan   Aridi
Title: Basic Mathematics

Area:
Country: United States
Program:
Avialable for Download: Yes

Table of Content

Introduction:

A before-and-after-school program can provide children with many opportunities to experience math in their every day lives as well as reinforce math concepts the children are learning in school. Keep in mind that a primary function of a school-age program is to support children as they gain tools fore living. Math is one of these tools. There are every day problems that incorporate the need of understanding math concepts

How many children are here for snack today?

How many tables will we need to set up?

How many cans of juice we will need to prepare to serve to all children?

We have eight tables with six chairs at each table; is that enough?

How can we find out

Spontaneous activities occur when children need to add up scores during indoor or out doo games. They must use math to measure ingredients needed for a project or the cost of buying the materials

When children manipulate, count, and measure real objects, they develop concepts that the can eventually relate to numerals and equations A wide variety of Buttons of different sizes, shapes, and colors

Children can identify objects that have a given attribute, children can create a set that corresponds to a given number 10 or less, children can count the elements in a set up to 10 numbers.

Description

Children used one-to-one correspondence to compare groups of ten or less When using one-to-one correspondence, the group that has unmatched items remaining is said to have more. This Button Math extends this idea to two- digit numbers. While one- to- one correspondences still feasible, other methods of comparison are more efficient. One method is to use the digit in the tens place to determine which number is greater. However, if the tens are the same then the ones should be compared. Explain to children that is less than < means that there is not as much or as many of something. Allow the children to work in a small groups to plan skits to present to the class using this n ew term.

Provide an example for them such as gathering crayons and one child having less than another child Add the new term to the Math World Wall.

During a sharing time, help children build background knowledge about the concept of less. Have children consider situations with which they are familiar, such as taking a bath or brushing the teeth. Which would take less time brushing teeth or taking a bath? Of course brushing the teeth take less time than taking a bath. Children learned that the group does not have nough items to match is said to have less. The same strategy used to determine which of two numbers is greater is a useful strategy in this lesson. However, in this lesson the smaller number must be determined.

The digits in the tens place should be compared first. If one is less, then that number is less than the other number. If the tens are the same, then the ones digits should be compared. Use buttons to teach the math concepts of more than, less than, and equal. This lesson Can also be used to teach the concepts of sets and attributes.

Math background:
The ideas explored in this lesson will help children develop algebraic thinking about number relationships and expressions.

Is less than <, is greater than >, and is equal to =, are terms and symbols used to build number sentences or statements. 

- Example: 3 + 2 = 5, 5 > 3, and 2 < 6 are statements about numbers. The first statement interpreted as the answer to a problem will cause later confusion. The equal sign is used equivalence and should be taught to mean “ is the same as .“

General Recommendations:

To model and compare two digit numbers to determine which is greater or less. To use symbols for is greater than >, is less than <, is equal to =, to compare numbers. To use a number line to compare two-digit numbers to determine the number comes just before, just after or between other numbers. To use the problem solving skill use a model to solve problems.
To count forward and backward. To compare two numbers less than twenty to find the greater set. Started options:

For each children base- ten blocks, Review with children how to model a two – digit number using base – ten blocks. Ask children to show two numbers ( 19 and 11 ) on their workmate by using the tens and ones columns. Tell children to point to the greater number. Remind children to start in the tens column first to see which ten is greater. If the tens are the same, tell them to check the ones column. Write 19 > 11 on the board and explain that this is the greater than sign.

Essential Skills:

After this lesson children will :

· Make the connection between models, equations, and fact strategies.
· Model and compare two – digit numbers to determine which is less than <, equal to =,
or greater than >
· Model and compare two – digit numbers to determine the number that comes just
before, just after, or between other numbers.
· Count forward and backward.

Why learn this?
· Knowing the values of numbers will help you add and subtract accurately and will
help you to make comparisons between groups of things.
· Knowing how to identify and label groups will help you make accurate comparisons.
· Knowing how to use the signs for is less than, is equal to, and is greater than will help
you develop your ability to think algebraically.
· Solving problems may involve finding which number is greater or less.
· Counting helps you learn the order of numbers and will help you when begin adding or
subtracting larger numbers.

Materials needed:

· A wide variety of buttons of different sizes, shapes, and colors.
· Ten large cards, each with a different number one to ten written on it (optional).
· Sets of three cards ( one set for each group of three students) ; in each set there
Should be one card that has the word equal written on it, one that says less than,
and one that says more than.
· Dice ( one die per group of three students)
· BINGO cards ( see instructions in the Before the Lesson section below)
· Math journals ( optional)

The lesson: 

Before the lesson:
In advance of this activity, collect a bunch of buttons. Write on 3 * 5 cards some of the attributes that describe those uttons; write one attribute per card and be sure each button has at least two attribute cards that apply to it. Possible attributes ight include shape ( round, square………..), color ( white, blue, gold, silver, black, gray,…..), number of holes ( two- holed, three- holed………..), type of material ( Plastic, metal).

If you plan to end the lesson with a game of Button BINGO, you will need to create BINGO cards in advance. Do that by taking a blank BINGO template and, in the spots where the letters B-I-N-G-O and O would appear write in place of each letter one attribute of some buttons; for example, the five attributes might be white, round, four- holed, plastic, and gold.

The rest of the card ( where numbers usually appear) it totally blank; students will fill in hose spaces with buttons as you call out attributes.

Lesson Detail :

To start the Lesson, have each student choose a button. Randomly pull one of the 3 * 5  cards from your set of attribute cards, read the attribute, and ask students who have a button with that attribute to stand.

Call out, one at a time, the other attributes listed on the 3 * 5 cards. Call out attributes until everyone is standing.

Next, randomly distribute or allow students to select ten ( 10 ) buttons of different sizes, shapes, and colors.

Display a large card with a number between 1 and 10 on it. ( Option: Write a number between 1 and 10 on the board.)

Ask students to make a set with many buttons in it.

Did students count out the correct number of buttons?

Repeat this activity several times, each time displaying a different number.

Review the concepts of equal , more than, and less than. You might give students some group practice by displaying buttons on an overhead projector. Have students identify the number of buttons ( a number between 1 and 10) displayed on the overhead. Then ask them to identify how many buttons would be one less than and one greater than the number of buttons
displayed.

Next, arrange students into groups of three. You might do this by preparing ahead of time a group of three cards that have the outlines of two buttns drawn on them, a group of three cards with three buttons drawn on them, a group with four buttons, five, and so on….

Give each student one of the cards and have them find the other two students who have the same number of buttons on their cards.

When they have found their “ partners” the three students will form a group. Remind students that they are expected to follow group rules and behavior. Ask others for help, help others if they ask, share the work, and work quietly. You might call for one student in each group to gather materials, or you might pass out the materials students will need.

Give each group a die, and give each student in the group a card; one student will receive a card that says equal on it, another will receive a card that says less than, and the third student will receive a card that says more than. Tell the students they are going to use their buttons to make sets that are equal to, one more than, and one less than a number. Instruct each student to take one of the three cards labeled equal, more than, or less than. Identify in each group the student who selected the card that says equal on it. That student will roll the die, name the number showing ( 1 to 6 ) on the die, and make a set of that many buttons.

The student with the more than card will count out a set of buttons that has one more than the number that appears on the die.

The student with the less than card will make a set of buttons that has one less than the number on the die.

Have students take turns using different cards. That way, each student gets turns at rolling the die and making sets that are equal to, less than, and greater than the number rolled on the die.

If your students have math journals, they might draw the sets in their journals and label how many buttons are in each set.

Give students about fifteen minutes to do this as you circulate around the classroom making sure they are on task and grasping the concepts.

Lesson Closure:

When the activity is over, have students put away their materials and gather on the meeting carpet. If students have drawn pictures of their sets, you might have them share their journal drawings and explain their sets. Then introduce a game of “ Button BINGO.” Pass out a handful of buttons to each student. Provide prepared BINGO cards that have attributes of the buttons listed across the top. ( See instructions for creating BINGO cards in the Before the Lesson section above.) When the students are ready, call out an attribute and ask all students to find one button among those they have that matches that attribute. If they have such a button, they should place that button in the appropriate attribute column. The first student to fill a column wins the game.

After playing Button BINGO, ask questions to determine if students can name the number that comes before or after a specific number without using buttons.

For example,
- What number comes before four?
- What number comes after nine?

I use this lesson to give the children a chance to apply what they have learned about money. I also use it to provide variety and incentive during review of other skills.

- Purpose:
Students are often taught money skills through the use of worksheets. They’re seldom given a chance to apply the skills in a realistic manner and often become bored with the drill of worksheets. This lesson provides them with practice opportunities prior to going into the community to shop.

- Objectives: Students will be able to:

Determine how much money they have in hand.
Find and read the price of a product.
Determine which product they would like to buy.
Determine if they have enough money for the item.
Count out the exact change or determine how much change they are due.

- Resources / Materials:
Clean trash ( empty soup cans, cereal boxes, vegetables cans, ect.) and stickers to use as price tags on items or index cards with prices to label the shelf the item is on.

- Activities and Procedures:
1. Each child is given a set amount of change. The particular coins each is given is determined by which coins have already been introduced to them and which ones they have prior experience counting. Beginners start with pennies only.

2. Each child is given a set amount of work in any subject that they need extra practice on. I usually use computational math skills. How many problems need to be completed before visiting the store is determined on an individual basis by the difficulty of the work for each child and how long it will take them to complete it.

3. As the student completes the assigned number of problems (i.e. three addition problems), they bring the work and their change to the “ store” where they count their money and decide what to buy while the teacher corrects the problems. The teacher or a student helper is then the store clerk and takes the change from the student. The student must tell the clerk how much change they are due, if any. The student then returns to their seat and completes another three addition roblems or whatever their assignment is ) before returning to the store.

- Tying it all together:
After each child has progressed at least through counting quarters, I like to take them on a field trip to practice these skills in the community. Each child is responsible for paying the correct fare upon boarding the city bus and if they can bring a small mount of money, they can actually buy something in the store. If they can’t bring money they window shop and
compare prices.

This activity is good just before winter break as it affords the children a chance to shop for gifts without the family members around they want to buy for, although some years the children are not quite ready that soon in the school year.

Conclusion:

Using buttons to teach the math concepts of more than, less than, and equal to. This lesson can also be used to teach the concepts of sets attributes. When children manipulate, count, and measure real objects, they develop concepts that they
can eventually relate to numerals and equations. They need to hold objects in their hands, weigh, or count them so that the concepts of size and number are evident.

Spontaneous activities occur when children need to add up scores during indoor or out door games. They must use math to measure ingredients needed for a project or the cost of buying the materials.

When children manipulate, count, and measure real objects, they develop concepts that they can eventually relate to numerals and equations

A wide variety of Buttons of different sizes, shapes, and colors hildren can identify objects that have a given attribute, children can create a set that corresponds to a given number 10 or less, children can count the elements in a set up to 10
numbers

References:

Cheryl J. Pembroke- Webster

Elementary Special Education; Anchorage, Alaska (1989, p. 56

Hands-On Math ( Apple 2 Mac IBM )

Grover Beach, CA: Ventura Education Systems.

Primary, Intermediate, Advanced ( 1988, p. 67

Mindy Martincic, University of Pittsburgh in Johnstown.

Pennsylvania. (2000, p. 4)

Van Cleave, J. (1996, p. 202)

New York: John Wiley & Sons, Inc.

Wheeler, R. (1997, p. 92)

School age program. Albany, NY: Delmar Publishers.