the parent page page 1 of 40

Relevant Learning Objectives

Understand the properties of points, lines, and line segments. Perform the four operations with decimals. Record and interpret data using tables, graphs and charts. Use a variable to represent a given verbal expression. Determine the area of objects. Make decisions about how to approach problems and find solutions. Draw and classify two-dimensional shapes with up to ten sides. Analyze and generalize number patterns. Draw and/or identify the radius, circumference, and diameter of a circle. Find factors of numbers to 100 and determine primes and composites. Understand the magnitude of numbers and apply large numbers. Apply the four operations with fractions. Understand the concept of positive and negative numbers.

of 40The Parent Page

7/21/2009International Learning Corporation © 2009

Understand the properties of points, lines, and line segments. Students should be able to understand the properties of points, lines, and line segments. Tutorial: For this activity you will need:

A sheet of graph paper. You can pick this up in most school supply sections of local stores.

Have the student write the following definitions on a note card to keep for easy reference. On the back of the note card, have the student draw an example of each. He or she can use the example illustrated for reference. For the purpose of this tutorial, we will use the following definitions:

Point - A unique, singular place in space (our 3D world) or on a plane (such as a piece of paper). A couple of possible ways to represent a point are as a pencil mark (dot) on a piece of paper or a computer pixel on a computer screen. A point is sometimes represented as an ordered pair of numbers on a graph indicating a horizontal and vertical distance away from some starting point on the same graph.

You name a point using a capital letter. For example:

Line Segment - A special collection of points consisting of two known or given points (end points) and all of the points that lie directly between them on a straight line. This is usually pictured as a line with two bigger, solid points on the ends.

Line segments are named using their endpoints, with a line above. For example:

Line - This is similar to a line segment except that no endpoints are necessarily known or given. A line can be thought of as a special collection of points forming a straight line that continues on forever in two directions. This is usually pictured as a line with two arrows on the ends. You can name a line using any 2 points on the line. You can also name a line using a single lower case letter. For example:



Exercises Have the student write the name of each figure below on a piece of paper. Use the note cards if needed, but have him or her try to write the names without referring to the note cards first. Answers are listed below. 1.

2.

3.

Answers 1.

2.

3. Point G

Activity Have the student use the graph paper and make a dot (point) on one of the square corners somewhere near the upper left corner of the paper. The student should label this point "A." It will be the starting point for this activity. Starting at point "A," have the student "move" 5 units to the right and make another dot (point). The student should label this point "B." Now draw a horizontal line connecting the two points. This is line segment AB. Starting at point "B," the student should now move 5 units down and make another dot (point). Label this point "C." Draw a vertical line connecting points "B" and "C." This is line segment BC.

The student has now created one half of a square, containing three of its corners - points A, B, and C. To continue this activity, have the student start at point "C" and ask how far and in what direction we need to move to create point "D," the fourth corner of the square?



Have the student use the remaining areas of the graph paper to create line segments to form a triangle, rectangle, and pentagon in a similar method as described above.

Review:What are the differences between a point, line, and line segment? Draw an example of each.



Perform the four operations with decimals. Students should be able to perform addition, subtraction, multiplication and division with decimal numbers. Tutorial: Items needed for this activity:

Pencil and paper Note cards Calculator (optional)

First, have the student use note cards to write down the rules listed below for performing operations with decimals. On one note card, write the rules for adding decimals, on another, the rules for subtracting decimals, and so forth. Adding Decimal Numbers

Align the decimal numbers by putting the numbers being added in vertical format. Add the numbers in the same way you add whole numbers (numbers without

decimals). Put the decimal point in the column directly below the decimal points of the

numbers being added. Subtracting Decimal Numbers

Align the decimal numbers by putting the numbers being subtracted in vertical format.

Subtract the numbers in the same way you subtract whole numbers (numbers without decimals).

Put the decimal point in the column directly below the decimal points of the numbers being subtracted.

Check your answer using addition. Multiplying Decimal Numbers

Multiply the numbers just as you would multiply whole numbers. In order to determine where to put the decimal point in the answer, count the total

number of decimal places in both numbers being multiplied. Then start at the right and count left that number of decimal places.

Dividing Decimal Numbers

If the divisor is not a whole number, move the decimal point to the right in order to make it a whole number. In order to keep the same problem, we then move the decimal point the same number of places in the dividend.

Divide as if you are dividing whole numbers, until the answer terminates or repeats. Put the decimal point directly above the decimal point in the dividend. To check your answer, multiply the quotient by the divisor and if it equals the

dividend, then the answer is correct.

Using his or her note cards, have the student perform the following calculations. Have the student write down on his or her paper an estimate of the solution, keeping in mind the rules for operations. Once the student finds a solution, have the student compare it to his or her estimation and then have the student check his or her answers using a calculator.



Example 1: 63.756 + 36.3 = ?

Step 1: Write in vertical format and align the decimal point. Place zeroes in the bottom number to fill-in. Remember, that when you place zeroes on the far right side of the decimal point, the value remains the same.

Step 2: Perform addition. "Carry-over" the same as when adding whole numbers.

Answer: 100.056 Example 2:

373.157 - 82.37 = ? Step 1: Write in vertical format and align the decimal point.

Step 2: Perform subtraction. "Borrow" as needed as you would with whole number subtraction.


12.57 x 3.13= ?



Step 1: Multiply just as you would with whole number multiplication, then add the number of decimal places in both numbers. The sum of the decimal places is the number of decimal places in the solution.


Step 1: Make the divisor a whole number by moving the decimal point 1 place to the right. In order to keep the same problem, we move the decimal point the same number of places in the dividend.

Step 2: Divide as you would divide whole numbers until the answer terminates or repeats. Place the decimal point directly above the decimal point in the dividend.



Answer: 3.879375

Review:What are the rules when multiplying decimals? Write a example problem and solution for dividing decimals.



Record and interpret data using tables, graphs and charts. Students should be able to compare, record and interpret data using tables, graphs and charts. Tutorial: We use graphs, charts and tables to describe a variety of situations. We use these representations to give us a "snapshot" of groups of information as a whole. It is important that the student understand how to interpret and analyze information in graphic form. It is important to practice reading graphs, compare information using graphs, and record information in graph form. Use the following three activities to practice these skills with the student. Discussion questions follow the graphs. Activity 1 Mark kept records of the points he scored at each basketball game during January. He recorded the information on this graph.

What were his or her average points per game?



Did he improve each game?

(He improved during all games except one, the game on January 17th. We could possibly conclude that he didn’t play the entire game, he was sick that day, or maybe he was injured.)

What can the graph tell us as opposed to just reading the scores? (We can see in picture form Mark’s improvement each game, except for the one game on January 17th. It is easier to get a "snapshot" of his scores by looking at the line of the graph.)

Activity 2 Jolene created a bar graph to illustrate how much she spent on food and housing in January, February and March.



In which month did she spend the most on food? on housing? (She spent the most on food in March, and she spent the most on housing each month of February and March).

Which varied the most, the cost of housing or the cost of food? (The cost of food varied the most month to month, food varied by $100.00 from February to March, and housing varied only $20.00).

What is the average price of housing for January through March?

Activity 3 Use the information in the table to record the data in graph form. Jasmine is practicing for a marathon. Each day she adds a minute to her workout and records the time.



Just as an example, the student might record the data as follows:

Did she consistently improve each day?

(She improved all days except the day she ran for 12 minutes). On which day did she make the farthest distance?

(The day she ran for 15 minutes). What might you conclude about the day she ran for 12 minutes?

(She may have been sick or injured that day, or it could have been windy outside). How far would you predict she might run in 16 minutes? 17 minutes?

(Probably around 2 miles each time). For enhanced learning, have the student gather data about his or her own environment and record the information in graph form. For example, have the student gather information from family members about shoe size, favorite food, or how many hours they sleep each night. Help the student to choose a graph form that would appropriately illustrate the data. Additionally, have the student find graphs, charts, and tables in the newspaper or on the Internet. For example, the student might find a table of high and low temperatures for particular calendar dates for your town. Below are some suggestions for leading a discussion with the student about the information he or she might find:



What other forms might you use that would also give a "snapshot" of the information?

What is unusual or interesting about the data? Are there extreme values within the information (instances where the numbers vary

widely)? Would someone in a certain occupation use this information?

Review:On Jenna’s 7th birthday she wore a size 1 shoe. Each birthday she kept track of her shoe size and created the graph below to show the information.

Between which ages did her feet grow the most? Which year did her feet stop growing? How many sizes did she grow from age 10 to age 12?



Use a variable to represent a given verbal expression. Students should be able to use a variable to represent a given verbal expression. For example, 5 more than a number is a + 5. Tutorial: Items needed for this activity:

Paper and pencil Note cards

An important skill in mathematics is the ability to take a problem stated in "word form" and transform it to one that uses the numbers and symbols that people are more familiar with when doing math problems. In this tutorial you and the student will begin to look at this skill by taking small parts of word problems and transforming them into small parts of math problems, called expressions.

Ask the student to consider the following: "5 more than a number"

In order to make sense of this using math symbols, explain to the student that he or she needs a way to express both "a number" and "more than" mathematically. For "a number" we need a variable. A variable is just a letter (typically x) that serves as a placeholder for the amount of numbers we’re looking for, until we know them. Explain to the student that the "more than" part is just another way of saying addition. So, "5 more than a number" becomes:

x + 5

Have the student write down the following words on a note card, as well as what they might mean when transforming a word problem.

With these ideas, a variety of word problems can be changed to numbers and symbols. Go through the following example with the student, helping the student "build" a math expression.

Example 1:

"6 less than 3 times a number"



Step 1 Identify the key words: less than, times, a number

Step 2 Replace the key words with their mathematical equivalents. Important note: do the multiplication first! You’ll see why, below. "3 times a number" becomes:

3y

Remind the student that when using variables, writing them right next to a number (the coefficient) implies multiplication. That is, 3y means "3 times y."

Step 3 "6 less than" means subtract 6 from the expression. This is very important, and it is the place most students make mistakes. Make sure that the student understands this point in particular. So, the problem becomes:

3y - 6

This is clearly "6 less than 3 times a number."

Note: Point out to the student that this is NOT the same as

6 - 3y

which would be written out as "three times a number less than 6."

This would be a good time to explain to the student that possible errors of this type will most likely occur when subtraction is involved. The student should pay special attention in those instances to avoid any mistakes.

Let’s try another example. Ask the student to independently write the expression, referring to his or her note card if needed. Help the student after approximately 5 minutes if he or she is having difficulty. Example 2: "5 more than 2 times a number" Step 1 Identify the key words: more than, times, a number

Step 2 Replace the key words with their mathematical equivalents. Important note: do the multiplication first! You’ll see why, below. "2 times a number" becomes:

2a

Step 3 "5 more than" means add 5 to the expression. The problem becomes:



2a + 5

Review:Represent the following as an expression: 5 times some number is equal to 20.



Determine the area of objects. Students should be able to determine the area of objects. Tutorial: Items Needed For This Activity:

Paper and pencil Begin by explaining to the student the definition of area. Area is the square units needed to cover a shape. Area is the measurement "inside" a shape (remember that perimeter is the measure "around" an object). We measure area in square units, typically square centimeters, square meters, square inches, etc. Activity: We use formulas for calculating areas. In order to understand and memorize the formulas, have the student write each of the following on separate note cards. On the back of each note card, he or she should draw the object and label it as shown below:

Area of a Square:

Area of a Rectangle: bh

Area of a Triangle:



Area of a Circle:

Now that the student has been introduced to the idea that we have formulas to find the area of objects, work through the following examples using his or her note cards. Quick Review: A letter and/or number next to each other means we multiply each, for example:

Also, when a number or letter is squared, you multiply that number or letter by itself. For example:

Exercise 1 Determine the area of the square below.

Solution You can find the area of a square using the rectangle formula. However, since the base and height are always the same for a square, the area of a square is equal to the length of one side squared. Therefore:

Exercise 2 Determine the area of the rectangle below.



Solution The area of a rectangle is the product of the base multiplied by height. Sometimes, the formula for a rectangle will be stated as length multiplied by width. Therefore, we can substitute our values into the formula for a rectangle as follows:

Exercise 3 Determine the area of the triangle below with a base of 5.2 cm and height of 4.2 cm. Round your answer to the nearest tenth.

Solution Using the formula written on the note cards, we determine the area of a triangle as follows:

Exercise 4 Determine the area of the circle below. Round your answer to the nearest tenth.



Solution

Review:Determine the area of a triangle with a base equal to 5 inches and a height equal to 4 inches.



Make decisions about how to approach problems and find solutions. Students should be able to make decisions about how to approach problems and use those strategies to determine solutions. Tutorial: For this activity, you will need the following:

A piece of scratch paper Note cards

Problem-solving strategies will be important skills for the student to have not only in his or her daily life, but also in any career the student might choose. There is often more than one strategy for solving logic problems and word problems. Ask the student to think of the different strategies he or she uses for solving word problems and write them down on a piece of paper. Help the student to come up with strategies by asking questions such as, "What is the first thing you do when you start an addition problem?" We want the student to say something like "I read the problem and think about what the answer might be." Continue to help the student determine what his or her own problem solving strategies are. Next, discuss the following list of strategies with the student. Then, using a note card, ask the student to write down the strategies that he or she has come up with along with the strategies listed below:

First, determine exactly what the problem is asking you to solve for (the unknown). Come up with a plan to solve the problem by analyzing the information: Write down all of the "knowns." Underline important information within the problem. Convert the problem into a math problem, if possible, using an equation. Draw pictures and/or graphs and label all of the "knowns." Determine information that is unnecessary.

Solve the problem. Then, analyze your solution and determine if it is a reasonable solution to the problem by looking back at the original problem.

Activity The purpose of the following activity is for the student to develop and apply problem-solving skills to an elementary logic problem. Encourage the student to use the problem-solving strategies listed on his or her note cards and to be patient in finding a plan to find the solution. Consider the following situation: I have a horse. I asked three people to guess what color it is. Person 1 said, "I guess it is not black." Person 2 said, "It is either brown or gray." Person 3 said, "I know it is brown." After they made their guesses, I said, "At least one of you is right and at least one of you is wrong."



So, what is the color of my horse - black, brown, or gray? You can summarize the information as follows: Person 1: Not Black Person 2: Brown or Gray Person 3: Brown Use the scratch paper and make a chart of all possibilities. You will find your solution when the color chosen for the horse results in at least one correct and at least one incorrect response from the three people. Finally, ask the student to explain his or her thought process and why he or she set up the problem in a particular way. The student should also defend his or her solution and offer at least one supporting argument so that you know he or she didn’t guess! Answer: The horse is gray. Solution: There are many ways the student could come up with a solution. Below is a possible way to determine a solution: Let’s consider if the answer is black: Person 1’s statement would be wrong. Person 2’s statement would be wrong. Person 3’s statement would be wrong. So we know the color of the horse is not black because we need at least one right statement and at least one wrong statement. Let’s consider if the answer is brown: Person 1’s statement would be right. Person 2’s statement would be right. Person 3’s statement would be right. Again, we do not have one right statement and one wrong statement. At this point we can conclude that the color of the horse is gray. Let’s test that solution: The horse is gray: Person 1’s statement would be right. Person 2’s statement would be right. Person 3’s statement would be wrong. Gray is the correct solution.

Review:Solve the following problem: 5 of the classes in your grade are going on a field trip to the amusement park.



There are 147 students, 5 teachers, and 5 chaperones. If each bus can hold 50 people, how many buses will be needed? Check your answer!



Draw and classify two-dimensional shapes with up to ten sides. Students should be able to draw and classify two-dimensional shapes with up to ten sides. They should understand the mathematical terms related to these shapes, such as quadrilateral, trapezoid, decagon, etc. Tutorial: During middle and high school, the student will take geometry classes. He or she will learn skills now, however, necessary to meet success in those later classes. One of the skills the student will need is an understanding of shapes. At this level, the student will already know his or her basic shapes: square, triangle, circle, etc. The student will probably have seen other shapes, too, although he or she might not remember their names and definitions. Help the student learn these more complex shapes by creating charts and flash cards to use for reference. Activity: Shapes & Names Chart For this activity you will need:

Poster board, piece of cardboard, or large sheet of butcher paper Markers Ruler Note cards

Go over the following definitions with the student. Look at the chart below as you discuss the different shapes and mathematical terms. Activity: Shapes & Names Chart For this activity you will need:

Poster board, piece of cardboard, or large sheet of butcher paper Markers Ruler Note cards

Go over the following definitions with your daughter. Look at the chart below as you discuss the different shapes and mathematical terms. Shapes plane figure: a flat, two-dimensional figure that lies in a plane polygon: closed figure formed by joining three or more line segments; each segment connects with two other segments quadrilateral: a polygon with four sides

Types of Quadrilaterals parallelogram: 2 pairs of parallel sides rectangle: 4 right angles square: 4 right angles and 4 sides of the same length rhombus: 4 sides of equal length

trapezoid - 1 pair of parallel sides Other Polygons (Not Quadrilaterals)

triangle: 3-sided figure pentagon: 5-sided figure



hexagon: 6-sided figure heptagon: 7-sided figure octagon: 8-sided figure nonagon: 9-sided figure decagon: 10-sided figure

Mathematical Terms Used to Describe Figures: side: line segment in a polygon vertex: end point where two line segments meet diagonal: line segment that connects two non-consecutive vertices

Once you’ve discussed the chart, the student can recreate it. Using the poster board and markers, the student should copy the chart. Encourage him or her to use a ruler to draw the shapes so they look as accurate as possible. You can post the chart where ever the student completes homework. Next, use the note cards to create flash cards of the different shapes and terms. Shape flash cards should look like the example below, with the shape drawn on one side, and the information about the shape on the opposite side.



Flashcards are a quick and easy way to learn math facts. You can use the flashcards for a quick review of shapes, particularly if the student has an upcoming test or quiz at school.

Review:Name and draw 5 different figures that have up to 10 sides. Then describe the attributes/characteristics of each figure.



Analyze and generalize number patterns. Students should be able to analyze and generalize number patterns such as: 1,4,9,16... are squares of the numbers 1,2,3,4... Tutorial:

Working with number patterns is more of an art than many things in math. Remind the student that much of the work with number patterns involves some experimentation to begin with. Have the student begin by trying the basic operations (addition, subtraction, multiplication, division) on some of the first few numbers in order to find the next number. For example, can the student add 3 to the first number to get the second? This is a good way to start thinking about what the pattern is all about.

However, in addition to this trial and error method, there is a little tool available to the student that can be quite helpful.

Consider the following image:

These are the first 7 rows of Pascal’s Triangle. If you look closely, you will notice that each new row is generated by starting with a "1", and then adding together two numbers from the previous row directly above in order to generate a new number in the current row.

Pascal’s Triangle has many applications. In particular, the student can use the rows, or diagonals in special ways to identify and understand some special number patterns.

Consider the following number pattern:

1, 1, 2, 3, 5, 8, 13, 21, ___, ___, ___

Have the student determine how this pattern is generated, and what the next three numbers should be. Apply the trial and error method as presented here, as well as use Pascal’s Triangle below to obtain a result.

Step 1 Start off by examining the first two numbers in the sequence: 1, 1. Performing addition yields the number 2 - the next number in the sequence. This is a good sign.

Step 2



Examine the 2nd and 3rd numbers in the sequence - 1, 2. Adding them together yields the number 3 - the next number in the sequence. This is probably the key to the pattern, but let’s try one more.

Step 3 Add together the 3rd and 4th numbers in the sequence to see if you get the fifth number. So, does 2 + 3 = 5? Yes!

Step 4 Adding together the previous two numbers in order to get the next number generates this pattern. That means that the next three numbers are: 34, 55, and 89.

Answer: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

Pascal’s Triangle can also be used to find the numbers in this pattern.

Point out to the student that starting with the first number on the left of each row, and using the diagonals as in the picture above, the number pattern in the problem is being created using addition: 1, 1, 2, 3, 5, 8, 13…

This would be a good time to let the student know that the pattern used in this example is a famous one in the world of mathematics. It is known as the Fibonacci Sequence, and can be studied as an independent activity to gain a better understanding of number patterns.

More Practice Have the student create Pascal’s Triangle on a sheet of paper out to 10 rows. This will allow him or her to begin to understand how the triangle is constructed. The student can add the completed triangle to a group of reference materials that he or she should already be accumulating as a study aid.

Review:What is the next number in the pattern? 1, 4, 9, 16, __



Draw and/or identify the radius, circumference, and diameter of a circle. Students should be able to draw and/or identify radius, circumference, and diameter of a circle. Tutorial: For this tutorial, you will need the following:

Paper Pencil Note cards A ruler or item with a straight edge (such as a notebook or textbook) Circular paper plate

Activity 1 Have the student write the following words, their definitions, and drawings of each on separate note cards. Radius: A line segment connecting the center to a point on the circle. Diameter: A line segment from one point on the circle, through the center of the circle, connecting to another point on the circle. The diameter of a circle is twice the length of a radius. Circumference: The circumference is the length around a circle.

Have the student practice using the cards with the word face-up first, and then by identifying the term from the picture/definition (on the other side of the card). Once the student has learned the terminology, move on to Activity 2.



Activity 2 Take out the paper plate. Have the student label the circumference of the paper plate (the outer edge of the circle) and then mark the center of the paper plate. Have him or her draw and label the diameter on the paper plate by drawing a straight line (with the ruler or straight edge). Have the student measure and record the length of the diameter on a piece of paper. Next, have him or her draw several radii from the center of the paper plate to the outer edge of the circle, and measure and record their length. The distance should be the same for all radii. Ask the student if he or she notices any relationship between the length of the radius and the length of the diameter. After you have given the student time to think about it, explain that the diameter is always twice the length of the radius.

Review:Which color is the radius? Which color is the diameter? Which color is the circumference?



Find factors of numbers to 100 and determine primes and composites. Students should be able to find factors of numbers to 100 and determine primes and composites. Tutorial: For this activity you will need:

Paper and pencil Note cards Division flashcards (optional)

For this activity, the student should have a solid foundation in short division (division that can be done in your head.) In addition, the student will need to be able to define and work with factors, prime, and composite numbers.

Short Division Review:

The student should be able to solve the problems below quickly, without paper. If not, work with flashcards or computer-assisted drills. This will prepare the student for the ensuing activity on primes and factors.

Prime Numbers, Factors, and Composite Numbers

Have the student write down the definitions below on a note card and memorize the concepts. He or she should be able to give you examples of a factor of 45, a prime number, and a composite number greater than 15.

Factor: A number that will divide into another number without a remainder. Some examples: 2 is a factor of 80, 2 divides into 80 with a result of 40 with no remainder, while 3 is not a factor of 80 as the result is 26 with a remainder of 2.

Prime Number: A number that is only divisible by 1 and itself. It only has two factors. Some examples: 2 (the only even prime), 3, 5, 7, 11, 13...

Composite Number: A number that has more than two factors. Some examples: 9 (factors are 1, 3 and 9), 18 (factors are 1, 2, 3, 6, 9 and 18)

Activity 1: Factoring Have the student find all the factors of 15. We know that 1 and 15 are factors, so now the student will use prime numbers to simplify the activity to see if there are additional factors. Since 15 is an odd number, the student should realize that 2 will not be a factor; begin with 3. Three divides into 15 five times with no remainder, which means both 3 and 5 are factors of 15. Are there any more? The student should check to see if the next prime, 7, will divide into 15 without having a remainder. It doesn’t, so 7 is not a factor. The student can stop now, as you only need to try numbers that are one-half or less than one-half of the number we are working with. In this case, 7 is our stopping number.



Answer: 1, 3, 5, and 15 are factors of 15.

Activity 2: Factoring Trees

Have the student use his or her knowledge of prime numbers to determine all factors of a number using a factor tree, as both a solid visual and a check at the end.

Example: Find the factors of 16. Step 1: Put 16 at the center of the page (this is the top of the tree).

Step 2: See if a prime number will divide into 16 evenly. (The student should begin with the smallest prime which is 2.) If it does, the student should place the number on the left side of the next row, and the result on the right, to balance the tree.

Step 3: Now the student should look at the second row to see if either number can be factored further. If so, create a third row.

Step 4: The student should create a fourth row if possible.

Step 5: Create a fifth row if possible. It isn’t possible, so the prime factors of 16 are 2, 2, 2, 2. To check his or her work, multiply across each row. The result must always be 16. Prime or Composite Activity: While driving in your car, have a family contest to determine if the last two numbers of a license plate form a prime or composite number. Game rules: player must call out the number and immediately say prime or composite; if



composite, they need to provide the SMALLEST prime factor for an additional point. A wrong answer costs the player a point and allows another person the chance to answer.

Examples: 5: answer PRIME ---1 point 70: answer COMPOSITE - 2 is the smallest prime factor --- 2 points 81: answer COMPOSITE - 9 is the smallest prime factor --- 1 point (3 is the

smallest) - one point deducted and second player can get a point by saying that the smallest prime number is 3.

Traveling will become a fun game with educational value.

Review:Determine if each of the following is a prime number or a composite number? 81 9 36 Find all factors for the number 18.



Understand the magnitude of numbers and apply large numbers. Students should be able to understand the magnitude of numbers and apply large numbers. Tutorial: Items needed for this activity:

Pencil and paper Newspapers, magazines or the Internet

It is important for students to comprehend how very large numbers are used in our world. For example, the post office uses very large numbers for zip codes and house numbers. Banks use very large numbers to represent how much money some people have in their account. We use very large numbers to represent how many people live in a city or country. Ask the student to think of ways that large numbers are used. Use the examples above and see if the student can think of ways on his or her own. As the student comes up with examples, you might use some of the following questions for further discussion: Are those numbers used to show order (as in street numbers), or are those numbers assigned to show size (as in money)? If we didn’t use numbers, can you think of a better way to represent that (would letters work, etc)? And why or why not?

Copy or show the above to the student. Using the newspaper or browsing the Internet, find some examples of very large numbers. Have the student say the numbers using the chart to aid in verbalizing large numbers. Ask the student to tell you how the numbers are used. Are they used to show size, amounts, to order things, or randomly, as they are when used for the numbers pinned to marathon runners shirts? Again, have the student brainstorm other ways in which these numbers could be represented and why or why not that would work.



Review:Identify the place value of each digit in the following numbers: 1 427 5,782,490



Apply the four operations with fractions. Students should be able to apply addition, subtraction, multiplication and division with fractions. Tutorial:

As you begin this skill, ask the student to review his or her knowledge of the rules of operations for fractions. Recall that these rules state that for addition and subtraction, both fractions must possess a common denominator. If they don’t, they must be modified so that their denominators are the same. Once the denominators are the same, both numerators are added (or subtracted, depending on the problem) but both denominators remain unchanged - they are not added or subtracted further. For multiplication, the two numerators are multiplied to form a new numerator, and the two denominators are multiplied to form a new denominator. For division, the second, or bottom fraction is inverted (denominator is now numerator, and numerator becomes denominator). Then, the rules for multiplication are applied to obtain a result. Be aware that the most troublesome fraction problems for students involve addition and subtraction of fractions with different denominators. Getting a common denominator is the trouble point for most students. Point this out to the student and work through the following example: Example 1: Addition of Unlike Denominators:

Step 1: Observe that the denominators (bottom numbers) are not equal. A common denominator can ALWAYS be determined by multiplying the two different denominators. It may not always be the Least Common Denominator (LCM) but it will work to solve the problem. In this case, the common denominator is 15 (3x5=15). Step 2: Modify all fractions so that their denominators are equal. In step 1, we determined that the common denominator would be 15. That involves multiplying the top fraction by 5, and the bottom fraction by 3. Doing so yields:



Step 3: Observe that the denominators are now equal. Add the numerators and leave the denominators as they are.

A subtraction problem would proceed similarly, but you would subtract the numerators after finding a common denominator. Example 2: Multiplication:

Step 1: Multiply the numerators. 3 x 7 = 21. 21 is the numerator of the result. Step 2: Multiply the denominators. 5 x 11 = 55. 55 is the denominator of the result. Step 3: Write the numerator and denominator obtained above as the answer of the problem.

Example 3: Division:

Step 1:



Invert the second fraction.

Step 2: Change the problem to multiplication.

Step 3: Multiply the numerators. 1 x 7 = 7. 7 is the numerator of the result. Step 4: Multiply the denominators. 5 x 2 = 10. 10 is the denominator of the result. Step 5: Write the numerator and denominator obtained above as the answer of the problem.

Additional Sample Problems: Have the student complete the following sample problems applying the rules for operations with fractions described above.

Remind the student that learning fractions will help him or her in many endeavors. It will aid in completing educational goals, as well as other areas of interest. If the student has interests in the culinary arts (chef), sciences (chemist), or even business (analyst), a solid understanding of fractions will serve him or her well.

Review:What is 1/9 + 3/4? What is 3/4 - 1/3? What is 3/5 x 1/3? What is 2/3 divided by 5/7?



Understand the concept of positive and negative numbers. Students should be able to understand the concept of positive and negative numbers. Tutorial:

Begin by discussing the concept of negative numbers. Use ideas such as temperature and banking accounts. Lead the discussion by asking questions such as the following:

If you withdraw more money out of your savings account than you have in it, how is that number represented?

How do we show the temperature when it goes below 0?

NOTE: Use language and phrasing that the student will understand. Use examples that will be familiar, such as overdrawing from his or her lunch account at school or the amount of an allowance rather than a savings account.

A simple way to help the student understand the concept of negative numbers is to use a number line. Draw a number line on a piece of paper or copy and paste the number line below. HINT: Draw a number line with a black marker and use a pencil to draw arrows and points as you go through the exercises. Then you can erase your pencil lines along the number line.

Use the number line to lead discussions and answer questions involving negative numbers. Below are some samples of questions and discussions. If you feel the student needs or wants more practice, vary the exercises below. It is sometimes helpful to work through one or two problems with together, and then ask the student to show you how to come to the answer on his or her own. Read the following problem with the student and find the answer using a number line.

If you give me $5.00 for a game and I go to the store and pick it up and it costs $8.00, how much money do you owe me? (You will have negative this amount of money.)

Begin by placing your pencil on the positive 5 number. Move the pencil over to the left 8 places. The pencil will land on negative 3, written as -3.

Discuss with the student that positive numbers go to the right, so when we add numbers we go to the right. Negative numbers go to the left, so when we subtract numbers we move to the left.

Continue with similar questions until you feel the student grasps the concept of negative



numbers. Below is another sample question:

If the temperature is 8 degrees, and then the temperature drops 20 degrees, what is the temperature?

Use the number line to illustrate the answer. The answer is -12.

Discuss with the student the symbols for positive and negative numbers. Negative numbers are shown by a negative (-) sign. The sign is the same sign as the subtraction symbol because they mean the same thing. Positive numbers are shown by a positive (+) sign. Discuss the idea that we use a positive sign when it is necessary to differentiate or show that a number is not a negative number. If there is a number with no sign in front of it, we assume it is positive (+). For example, when you make a purchase, the number that is the price of an item does not have a + sign in front of it, but we know it is a positive number. This idea will be important when the student begins to perform operations with positive and negative numbers.

Enhanced Learning

Use the previous examples and write the problems in written subtraction form. Discuss these concepts with the student as preparation for addition and subtraction with positive and negative numbers.

5 - 8 = -3 can also be written as: 5 + -8 = -3

Note: Often there are parentheses put around the -8 to separate it, and it would be written as 5 + (-8) = -3

When subtracting a number, it’s the same as adding a negative number.

10 - 7 would be 10 + (-7) and: 8 - 3 would be 8 + (-3)

Illustrate the above examples using the number line.

Review:What type of number would represent a number less than 0? How are positive numbers different from negative numbers? Which way on the number line would you move (left or right) if you were counting negative numbers?



the parent page page 1 of 40

Documents