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PAGE CONTENTS
#1 Multiplication; #2 Division; #3 Time; #4 Number sense (Place Value); #5 Decimals; #6 Fractions; #7 Statistics (Plot,Graph,Medium,Mode,Mean);
#8 Money; #9 Geometry; #10 Measurement; #11 Ratio & Probability


Lesson # 1

Multiplication
multiplication.jpg

Here we will be learning about how to multiply using the expanded algorithm, along with arrays, properties of multiplication, factors, composite and prime numbers, and multiples.
external image lightbulb.gif Multiplication is a simpler way to do repeated addition. For example: 4 x 6 is easier than 4 + 4 + 4 + 4 + 4 + 4. You are also less likely to make a careless error using multiplication than if you use repeated addition.
external image lightbulb.gif An array is a way of ordering objects in rows and columns to make a rectangular shape. In an array, all the rows are equal to each other and all the columns are equal to each other and that makes a rectangular shape. For example:


external image array.gif
external image MultiplicationArray2.png









external image lightbulb.gif The zero property of multiplication is that any factor multiplied by 0 equals 0. For example:
5 x 0 = 0

external image lightbulb.gif The identity property of multiplication is that any factor multiplied by 1 equals the original factor. For example: 3 x 1 = 3
external image lightbulb.gif The commutative property of multiplication is that two factors can be multiplied in either order and give the same answer. For example: 7 x 2 = 2 x 7
external image lightbulb.gif The associative property of multiplication is that three or more factors can be multiplied in different groups and still give the same answer. For example: (4 x 5) x 6 = 4 x (5 x 6)
external image lightbulb.gif A number is a factor of another number if it divides into it evenly without a remainder. To find factors of a number you can make a factor rainbow. See the example below: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

external image rainbow6_flashing_stars.gif


1 2 3 4 6 8 12 24
external image lightbulb.gif Prime numbers are numbers that can only be divided evenly by 1 and themselves. For example: 7 is a prime number because it only has 2 factors. These factors and 1 and 7.
external image lightbulb.gif Composite numbers are numbers that have more than 2 factors. For example: 4 is a composite number because its factors are 1, 2, and 4.
external image lightbulb.gif Since 0 has no factors it is not prime or composite.
external image lightbulb.gif Since 1 has only 1 factor it is not prime or composite.
external image lightbulb.gif A multiple can be made by multiplying a number. For examples: some multiples of 6 are 6, 12, 18, 24, 30, 36 etc because 1 x 6 = 6, 2 x 6 = 12, 3 x 6 = 18, 4 x 6 = 24, 5 x 6 = 30, 6 x 6 = 36, etc.
external image lightbulb.gif When we multiply we can use the expanded multiplication algorithm. See example below:


2 5 4
X 3
1 2 (3 ones x 4 ones)
1 5 0 (3 ones x 5 tens)
+ 6 0 0 (3 ones x 2 hundreds)
7 6 2


To practice multiplying.

http://www.prongo.com/math/multiplication.html

To practice factors and multiples.
http://www.bbc.co.uk/education/mathsfile/shockwave/games/gridgame.html

To practice multiplication facts.
http://www.crickweb.co.uk/assets/resources/flash.php?&file=Quiz-Times-Tables

To practice multiples.
http://www.tki.org.nz/r/wick_ed/maths/interactives_matrix.php

To practice using a multiplication grid.
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/multiplication/timestables/flash1.shtml

To practice multiplication facts.
http://www.multiplication.com/interactive_games.htm




Lesson # 2

Division
external image division%20sign.gif

Here we will be learning about how to divide using the expanded algorith for division. We will also be learning about divisibility rules.
external image lightbulb.gif When we know how many groups there are and how many things are to be shared, but we don't know how many are in each group, we divide to share equally.
external image lightbulb.gif
Division is the inverse of multiplication. Inverse operations undo each other. For example: 5 x 20 = 100 and 100 divided by 20 = 5.
external image lightbulb.gif Division is a simpler way to do repeated subtraction.
external image lightbulb.gif Divisibility Rules:

Number
Divisibility Rule
2
All even numbers or all numbers with 0, 2, 4, 6, or 8 in the ones place.
5
All whole numbers with 5 or 0 in the ones place.
10
All whole numbers with 0 in the ones place.
3
Any whole number whose digits add up to a multiple of 3.
For example: 204 is divisible by 3 because 2 + 0 + 4 = 6 and 6 is a multiple of 3 because 2 x 3 = 6.

external image lightbulb.gif Any number, except 0, is divisible by 1 and itself. For example: 30 divided by 1 = 30 and 30 divided by 30 = 1.
external image lightbulb.gif Division of 0 is a special case of divisibility because any number, except 0, will divide into 0. Zero divided by any number, except 0, is zero. For example: 0 divided by 3 = 0.
external image lightbulb.gif Division by 0 cannot be done.
external image lightbulb.gif When we divide we can use the expanded division algorithm. Go to the Click Me button below for expanded algorithm power point to see how to use the division algorithm.


Expanded Algorithm Power Point ---Located in teacher's file


To practice division facts.
http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html

To practice division facts.
http://www.oswego.org/ocsd-web/games/Mathmagician/mathsdiv.html

To practice completing division equations.
http://www.oswego.org/ocsd-web/games/SumSense/sumdiv.html



Lesson #3



Time

Aclock.jpg

In this time unit you will be learning how to tell time and how to find elapsed time.
lightbulb.gifTime on a clock can be measured in seconds, minutes, and hours.

60 seconds =
1 minute
60 minutes =
1 hour
15 minutes =
¼ of an hour
30 minutes =
½ of an hour

lightbulb.gifClocks move in a clockwise movement.
lightbulb.gifa.m. is from 12:00 midnight to 11:59 in the morning.
lightbulb.gifp.m. is from 12:00 in the afternoon to 11:59 at night.
lightbulb.gifClocks have a short hand to tell the hour and a long hand to tell the minute.
lightbulb.gifEach number on the clock represents 5 minutes.



Bclock%20face.gif


lightbulb.gifSteps to telling time:

1. Look at the hour hand. The hour hand on the clock above shows the hour is 1:00.
2. Look at the minute hand. The minute hand on the clock below shows that 15 minutes have gone by past the hour. To find the minutes you skip count each number on the clock by 5. The minute hand is on the 3 so 5 + 5 + 5 = 15.
3. Put the hour and the minute together to get the time. The clock below shows 1:15.


Cclock_hours_min_1_15.gif

4. The lines between the numbers stand for 1 minute. On the clock below the hour is 3:00. Skip counting by the numbers is 35 minutes. There is 1 line past the 7 so we add 1 more minute. 3:00 + 35 minutes + 1 minute = 3:36.


external image clock%202.bmp

lightbulb.gifElapsed time is how much time has passed or the amount of time we have to wait for something to happen. The steps to telling elapsed time are:

DDLLclock%208.gifEERRclock%201%20thirty.gif

1. The first clock shows 8:00. The second clock shows 1:30.
2. First you count how many hours have passed. 8:00 + 1 hr = 9:00, 9:00 + 1 hr = 10:00, 10:00 + 1 hr = 11:00, 11:00 + 1 hr = 12:00, and 12:00 + 1 hr = 1:00. So 1 + 1 + 1 + 1 + 1 = 5 hours have passed.
3. Next I count how many minutes have passed. I start at the 5 and skip count until I reach the 6.
5 + 5 + 5 + 5 + 5 + 5 = 30 minutes.

4. Then I add the hours to the minutes. 5 hours + 30 minutes = 5 hours 30 minutes.


Watch a time video:
http://www.kidsknowit.com/interactive-educational-movies/free-online-movies.php?movie=Telling%20Time


To review and practice time:
[After entering below link, click on the little red clock for the next page. The "check box" on the 4th page is faulty so do not type in answer. After readingthe page, go back to previous page, return forward page quickly. Try repeating this process until clicking the forward clock lets you bypass the pop up saying you need to answer that question. It is a glitch in the program that I do not have access to so that it can be fixed]
http://www.beaconlearningcenter.com/WebLessons/RightTime/default.htm


To practice telling time to hour & half hour:
http://www.oswego.org/ocsd-web/games/StopTheClock/sthec1.html

To practice telling time to five minutes:
http://www.oswego.org/ocsd-web/games/StopTheClock/sthec3.html

To practice telling time to the nearest minute:
http://www.oswego.org/ocsd-web/games/StopTheClock/sthec4.html

To practice elapsed time:
http://www.mathsyear2000.org/magnet/minus3/trains/index.html

To practice elapsed time in 1/2 hour:
http://www.numbernut.com/basic/activities/dates_quiz_timepast30.shtml

To practice elapsed time word problems:
http://marg.mhost.com/MathGr5/elapsedtime.htm





Lesson #4



Number Sense
placevalue.gif
In this unit we will be learning about place value. We will be developing our number sense so we can make common sense of mathematics.

lightbulb.gifNumbers are grouped in periods or families. The number families are ones, thousands, millions, etc. There are three places in each number family: ones, tens, and hundreds.

lightbulb.gifEach place is tens times as big as the place to its right. For example:



Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
100,000 x 10 = 1,000,000
10,000 x 10 = 100,000
1,000 x 10 = 10,000
100 x 10 = 1,000
10 x 10 = 100
1 x 10 = 10



lightbulb.gifThe standard form of a number is written in numbers. For example: 1,234,567.

lightbulb.gifThe word name of a number is written in words. For example: one million two hundred thirty four thousand five hundred sixty seven.

lightbulb.gifExpanded notation is the number written as the amount of each place value added together. For example: 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7.

lightbulb.gifYou can also use a place value mat to create a model of a number. For example:

place%20value%20mat.gifplace%20value%20mat%202.gif





Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones








lightbulb.gifPlace value and the digit determine the size of the number. For example: a 9 in the tens place is smaller than a 1 in the hundreds place because 9 tens = 90 and 1 hundred = 100.

lightbulb.gif< (is less than), = (is equal to ), and > (is greater than) are symbols used when we compare amounts. For example: 635,763 > 243,836.

lightbulb.gifWhen you compare numbers you start all the way to the left in the highest place value. A good strategy to help you is if you turn a piece of lined paper sideways and use the lines to help you line up the numbers.
paper.jpg

lightbulb.gifWe use our number sense when we round numbers. Rounded numbers end in one or more zeroes. To round a numbers, underline the place you want to round to. Look at the place to the right. If the digit is 5 or more, round up to the next number. If it is less than 5, the number stays the same. Put zeroes in the places to the right of the underlined number. For example: 37 is rounded to 40 because the 7 to the right of the 3 is more than five. 21 is rounded to 20 because the 1 to the right of the 2 is less than 5.
Watch a video about place value.
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/3_Place_Value/index.html

Practice naming the value of the digit.

http://www.teachrkids.com/examples/ones_tens_hundreds.asp?count=3&number_type=0&min_val=1&max_val=99999

Practice standard form.
http://www.mathsyear2000.org/magnet/kaleidoscope2/Crossnumber/index.html

Review and practice Expanded Notation.

http://www.coolmath4kids.com/addition/03-addition-lesson-place-values-01.html

Practice word names.
http://www.springboardmagazine.com/math/placevalue.htm

Practice less than.
http://www.mathsyear2000.org/magnet/minus3/hopscotch/index.html

Practice more than.
http://www.mathsyear2000.org/magnet/minus3/hopscotch/more1.html

Practice estimation.

http://questgarden.com/47/70/5/070308180610/index.htm
[The picture in the task section does not open, but the 2 in the process section will by clicking on the blank picture]
Creators glitch in link that I cannot fix. All the links work...if one is real slow loading, quit and try again
Technology is great but can be frustrating at times!




Lesson #5



Decimals

external image decimals.jpg

Here we will be learning about the decimal place values tenths, hundredths, and thousandths. We will also be comparing decimals and finding equivalent decimals.
external image lightbulb.gif A decimal point is a dot that comes between the whole number places and the decimal places in a number.
external image lightbulb.gif
All the digits to the right of the decimal point are less than 1 whole.
external image lightbulb.gif Decimals are special fractions with unwritten denominators of ten, a hundred, a thousand, etc. For example: if the decimal is 0.1 the 1 is in the tenths place. The fraction would be 1/10.
external image lightbulb.gif Decimals are parts of a whole. We can answer 3 questions to determine the decimal:



The Three Decimal Questions
1. What is the whole and how big is it?
2. Into how many equal parts has the whole been divided?
3. How many of the equal parts are we using?

external image lightbulb.gif Tenths are divided into 10 equal pieces. If all ten pieces are used than we have 1 whole.
external image lightbulb.gif Hundredths are divided into 100 equal pieces. Each row on a hundredths square has 10 equal pieces. If all hundred pieces are used than we have 1 whole.
external image lightbulb.gif Thousandths are divided into 1,000 equal pieces. Each row on a thousandths square has 100 equal pieces. If all thousand pieces are used than we have 1 whole.
external image decimal%20squares.jpg
external image lightbulb.gif The standard form of a decimal is written in numbers. For example: 0.1
external image lightbulb.gif The word name of a decimal is written in words. For example: one tenth
external image lightbulb.gif A decimal can be written in expanded notation. Expanded notation means to add the each place value together. For example: 0.1 + 0.2 + 0.3 = .123
external image lightbulb.gif A decimal amount can be modeled on a place value mat. For example:

external image tenths%20decimal%20number%20line.gif
This number line shows 1.9
external image lightbulb.gif A zero at the right end of a decimal doesn't change the amount, but it does change the way the amount is named. A decimal is named by the smallest decimal place. For example: 0.1 is one tenth and 0.10 is ten hundredths.
external image lightbulb.gif We can compare decimals and put them in order from least to greatest or greatest to least using the < (less than) or > (greater than) symbols.
external image lightbulb.gif Tenths > Hundredths > Thousandths. Remember not to focus on ten, hundred, or thousand part of the word names. Do not confuse their place value names with whole numbers. A tenth is larger than a hundredth and a hundredth is more than a thousandth. For example: 0.3 > 0.03 > 0.003
external image lightbulb.gif When you add and subtract decimals make sure to line up the decimals points and then add as usual. For example:


external image adding%20decimals.gif


external image lightbulb.gif Equivalent decimals are decimals that are equal. For example:

external image equivalent%20decimals.jpg
-----------------

To review and practice decimals.
http://www.bbc.co.uk/schools/ks2bitesize/maths/revision_bites/decimals.shtml

To practice adding decimals with number lines.
http://www.numbernut.com/advanced/activities/decimal_numline_add10th.shtml

To practice identifying decimals.
http://www.linkslearning.org/Teachers/1_Math/6_Learning_Resources/2_SuperMath/content/games/Decimal_Detective.htm

To practice putting decimals on number lines.
http://www.quizville.com/numberLineDecimalsArrow.php

To practice making the largest decimal.
http://www.decimalsquares.com/dsGames/games/placevalue.html

To practice comparing decimals.

http://www.crickweb.co.uk/assets/resources/flash.php?&file=washindex6

To practice identifying decimals.
http://www.decimalsquares.com/dsGames/games/beatclock.html

To practice decimals to the thousandths place.
http://www.numbernut.com/advanced/activities/decimal_4bar_1000th.shtml




Lesson #6



Fractions

external image half%20fraction.gif

Here we will be learning about the parts of a fraction, identifying fractions, equivalent fractions, and adding and subtracting fractions.
external image lightbulb.gif Fractions are parts of a whole. If an amount is divided into equal parts, or fair shares, we can understand and name fractions.
external image lightbulb.gif
The top number in a fraction is called a numerator. The bottom number in a fraction is called a denominator.


external image one%20sixth.gif


external image lightbulb.gif Fractions that have the same numerator and denominator always equal 1 whole. The examples below all equal 1 whole because the numerator and denominator are the same.
external image magic_1s.gif


external image lightbulb.gif Fraction names can be shown in numbers, words, or pictures.
external image lightbulb.gif To understand a fraction we need to answer 3 questions:


The Three Fraction Questions
What is the whole and how big is it?

Into how many equal parts has the whole been divided ?
The denominator of the fraction answers this question.
How many of the equal parts are we using?
The numerator of the fraction answers this question.
external image lightbulb.gif To identify fractions we count how many equal pieces have been used (numerator) and how many equal pieces there are altogether (denominator). For example: In the fraction below we used 2 equal pieces and there are 3 equal pieces altogether.


external image two%20thirds.gif


external image lightbulb.gif Equivalent fractions describe the same portion of a whole divided in different ways. For example: half a piece of paper can be represented as 1/2, 2/4, 3/6, 4/8, or 5/10, etc.
external image lightbulb.gif The circles below are examples of equivalent fractions. 1/2 and 3/6 are equivalent because 1 piece of the first circle equals 3 pieces of the second circle and 2 pieces of the first circle equals 6 pieces of the second circle.

external image circle_2piece.gif
external image circle_6piece.gif

external image lightbulb.gif Sometimes we can simplify or reduce fractions to make them easier to understand. When we simplify fractions we use the smallest numbers possible. You can divide the numerator and denominator by the same number to simplify. For example: below is an example of how to simplify 100/200.


external image simplify.gif


external image lightbulb.gif The easiest way to find a number you can divide into the numerator and denominator evenly to simply is to find the greatest common factor. For example: to simplify 27/108 find the greatest common factor of 27 and 108. Then divide the numerator and denominator by the factor to simplify.
The factors of 27 are 1, 3, 9, and 27.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
27 is the highest factor of the numbers 27 and 108 so we divide by 27.


external image 27_108_equals_1_4_work.gif


external image lightbulb.gif Adding and subtracting like fractions. Like fractions are fractions with the same denominator. For example: 1/6 and 3/6 are like fractions because both fractions have 6 as the denominator.
external image lightbulb.gif To add and subtract like fractions you add or subtract the numerator and the denominator stays the same. For example: in the problem below you would add the numerators (2+1=3) and the denominator stays the same (4). The answer is 3/4.

external image adding%20fractions.jpg
external image 7_8minus3_8equals.gif




external image lightbulb.gif Proper fractions are fractions in which the numerator is less than the denominator.



external image proper%20fraction.jpg


external image lightbulb.gif Improper fractions are fractions with a numerator equal to or greater than the denominator.


external image spacer.gif

external image improper%20fraction.jpg

external image lightbulb.gif A mixed number is a number that includes a whole number and a proper fraction.


external image mixed%20fraction.gif


external image lightbulb.gif In the real world we compare fractions to see which one is smaller or larger. If you were hungry would you want a slice of the first pizza below or the second pizza? Since the pieces in the first pizza are larger if you were hungry you would want a slice from this pizza.

external image pizza_4pieces.gif
external image pizza_10piece.gif

external image lightbulb.gif If you compare like fractions all you have to do is compare the numerators because the denominators are the same. For example: if you compare 3/8 to 7/8 you only need to compare the numerators 3 and 7.


external image 3_8lt7_8.gif


external image lightbulb.gif Like fractions can be ordered on a number line just as whole numbers can be ordered. In number line a the number line has been divided into 5ths. As you move to the right each fraction is larger. 1/5 < 2/5 < 3/5 < 4/5 < 5/5.


external image fraction%20number%20line.gif

To complete a fraction tutorial.
http://www.kidsolr.com/math/fractions.html


To review fractions.
http://math.rice.edu/~lanius/fractions/

To practice identifying fractions.
http://nlvm.usu.edu/en/nav/frames_asid_104_g_2_t_1.html

To practice adding fractions.
http://fen.com/studentactivities/MathSplat/mathsplat.htm

To practice comparing fractions.
http://www.bbc.co.uk/skillswise/numbers/fractiondecimalpercentage/fractions/introduction/flash3.shtml

To practice equivalent fractions.
http://www.freewebs.com/weddell/Equiv%20Fractions%20Contents.html

To practice identifying fractions.
http://www.learningmedia.co.nz/staticactivities/online_activities/flitting_with_fractions/

To practice 1/2 and 1/4 fractions.
http://www.oswego.org/ocsd-web/games/fractionflags/fractionflags.html

To practice fractions on a number line.
http://www.sums.co.uk/playground/n6a/playground.htm

To see a video on simplifying fractions.
http://www.hbschool.com/activity/show_me/e622.htm



Lesson #7



Statistics
external image graphing%202.gif external image graphing%203.gif






Here we will be learning about line plots and line graphs. We will also be learning how to interpret data by looking for clumps, holes, outliers, and the range, median, mode, and mean of data.

external image lightbulb.gif Statistics is a type of mathematics used to collect, organize, and display data for people to understand. Data are facts or information about people or things.
external image lightbulb.gif Line graphs show increases and decreases in a trend.


external image line%20graph%203.gif
external image line%20graph%205.jpg


external image lightbulb.gif
Line plots are a portion of a number line used as a quick way to organize and represent data as it is collected.


external image line%20plot%203.gif



external image lightbulb.gif A clump is a group of data pieces on the graph. The clump of the line plot is 0 – 4.
external image lightbulb.gif A hole is a place where there are no data pieces. The holes are at 5, 7, 9, 11, 12 and 15.
external image lightbulb.gif Outliers are pieces of data that are much larger or smaller than the rest of the data. The outliers are 13 or 14.
external image lightbulb.gif The mean is the total of the numbers divided by how many numbers there are.
1. Add up all the numbers: 7+ 9 + 11 + 6 + 13 + 6 + 6 + 3 + 11 = 72
2. Divide the answer by how many numbers there are: 72 divided by 9 = 8.
3. The mean is 8.
external image lightbulb.gif The median is the middle value.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. The number in the middle of the list is the median: 7.
3. If there are two middle values, the median is halfway between them:
3 6 6 6 7 8 9 11 11 13 – The median is 7.5
external image lightbulb.gif The mode is the value that appears the most.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. Look for the number that appears the most: 6.
external image lightbulb.gif The range is the difference between the biggest and the smallest number.
1. Put the numbers in order: 3 6 6 6 7 9 11 11 13
2. Subtract the smallest number from the biggest number: 13 – 3 = 10
3. The range is 10.


To practice making graphs.
http://nces.ed.gov/nceskids/createagraph/default.aspx

To practice interpreting data.
http://www.bbc.co.uk/schools/ks2bitesize/maths/revision_bites/interpretingdata.shtml

To practice line graphs.
http://www.quizville.com/linePlotMaking.php

To learn more about line plots.
http://www.glencoe.com/sites/texas/student/mathematics/assets/interactive_lab/mac2/M2_02/M2_02_dev_100.html

To practice mode, median, mean.
http://www.bbc.co.uk/schools/ks2bitesize/maths/activities/modemedianmean.shtml

To practice reading a graph.
http://www.haelmedia.com/html/mc_m4_001.html


Lesson #8



Money
external image piggy%20bank.jpgMoney is what we will be learning; how to count money, how to add and subtract money, and to determine the least amount of coins.
external image lightbulb.gif Review from 3rd grade: Penny = 1 cent, Nickel = 5 cents, Dimes = 10 cents, Quarters = 25 cents, and Half Dollars = 50 cents.
external image lightbulb.gif
When we count money, skip-counting is an easy way to find out how much money we have. When skip-counting coins, we count by 5's for nickels, 10's for dimes, 25's for quarters, and 50's for half dollars. When different coins are mixed together you count the coins with the largest value first. For example: the coins below would be counted as 10, 20, 30, 35, 40. The set of coins equals 40 cents.

external image dime.jpg
external image dime.jpgexternal image dime.jpgexternal image nickel.pngexternal image nickel.png







external image lightbulb.gif We also use skip-counting to make change or check to see if your change is correct. Skip-count up from the amount owed to the amount of money paid to find the change needed.
external image lightbulb.gif There are many different combinations of coins that can make up an amount of change, but we often want to get the fewest number of coins. If you went to the store and received a $1.00 in change would you rather have 100 pennies or a one dollar bill? In the example below the quarter is the fewest amount of coins that make 25 cents. It only takes 1 coin to make 25 cents with the quarter. It takes 3 coins to make 25 cents with the two dimes and one nickel.

external image quarter.jpgexternal image dime.jpgexternal image dime.jpgexternal image nickel.png






external image lightbulb.gif When you add and subtract money amounts remember to line up the decimals just like you did in the Decimal unit.


external image adding%20decimals.gif

To practice adding money.
http://www.beaconlearningcenter.com/WebLessons/ShowMeTheMoney/default.htm

To practice finding the amount of change.
http://www.mrnussbaum.com/cashout/index.html

To practice counting money.
http://www.mathplayground.com/count_the_money.html

To practice determining if you have enough money.

http://www.numbernut.com/advanced/activities/money_enough_lt1dollar.shtml

To practice determining money amounts.
http://www.beaconlearningcenter.com/WebLessons/LetsDoLunch/default.htm

To practice making change.
http://www.mathplayground.com/making_change.html






Lesson #9




Geometry


external image geometry.png


Here we will be learning about 2-dimensional and 3- dimensional shapes, lines, angles, transformations, coordinates, congruent or similar shapes, perimeter, and area.
external image lightbulb.gif A polygon is a closed figure made of three or more straight line segments. A regular polygon is a polygon whose sides and angles are equal.


external image polygons.jpg


external image lightbulb.gif Below are examples that are not polygons:
external image nonpolygon.gif
external image nonpolygon%202.gif

external image lightbulb.gif 2-dimensional and 3-dimensional shapes can be identified by their properties. Click on the links below to see the properties of these shapes.

To learn about the properties of 2-dimensional shapes.
http://www.mathleague.com/help/geometry/polygons.htm

To learn about the properties of 3-dimensional shapes.
http://www.studyzone.org/testprep/math4/e/geometric3d3l.cfm

external image lightbulb.gif Below are the types of geometric lines:
Line – a line is a series of points that make a straight path on and on in either direction.
Ray - a ray is a straight line that begins at a point and goes on and on in one direction.
Line Segment - is the part of a line between two points.

Horizontal Line - is a line that runs left to right, like the horizon.
Vertical Line - is a line that runs up and down, like a telephone pole.
Parallel Lines - are lines that never intersect and are always the same distance from each other at every point on the lines.
Intersecting Lines - are two lines that cross at only one point.
Perpendicular Lines - are two lines that intersect or meet and make four square or right angles.

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An angle is formed when two rays or line segments meet at a point called a vertex.
external image lightbulb.gif Any angle is a portion of a circle.
external image lightbulb.gif The three angles we will be learning about are right angles which are always 90 degrees, acute angles which are less than 90 degrees, and obtuse angles which are more than 90 degrees.

external image right%20angle.gif
external image acute%20angle.gif
external image obtuse%20angle.gif

external image lightbulb.gif A protractor is a tool for measuring the number of degrees in an angle.
external image Protractor.gif

external image lightbulb.gif To measure an angle with a protractor follow these steps:
  1. Make the lines of the angle longer if necessary.
  2. Line up the arrow or hole in the bottom of the protractor with the vertex of the angle. Remember the vertex is the point where the two lines of the angle meet.
  3. Line up the line at the bottom of the protractor with one side of the angle.
  4. Decide whether the angle is acute or obtuse to determine which number scale on the protractor to use.
  5. Find the number of degrees by finding where the side of the angle goes through a number on the protractor.
external image lightbulb.gif Congruent shapes are the same size and shape.


external image congruent%20shapes.gif


external image lightbulb.gif Similar shapes are the same shape, but might not be the same size.
external image triangle.png
external image triangle.png

external image lightbulb.gif There are 3 basic transformations: slides (translations), turns (rotations), and flips (reflections).
external image triangle%202.png
external image triangle%202.pngexternal image triangle%202.pngexternal image triangle%203.pngexternal image triangle%204.pngexternal image triangle%203.png






external image lightbulb.gif Remember that when we change the position of a shape it does not create a different shape. The shape is just in a different position.
external image lightbulb.gif Coordinates are a pair of numbers that locate a point. Coordinates are always written in the same order, so we call them ordered pairs. The first coordinate tells the sideways location and the second coordinate tells the up and down location. Remember go over then up. In the example below the coordinates are (7,4).


external image coordinate_system.jpg


external image lightbulb.gif The distance around a shape is the perimeter. The length of the perimeter of any polygon is the sum of the lengths of all the sides.

external image perimeter.gif2 + 2 + 1 + 1 + 1 + 1 = 8
external image lightbulb.gif Area is the amount of space inside a flat (2-dimensional) shape. Area has two dimensions: length and width. We measure area in square units. Area = length x width.


external image perimeter%202.gif5 x 5 = 25

external image lightbulb.gif 3-dimensional shapes have faces (sides), edges (lines where the sides join together), and vertices (corners). For example: the cube below has 6 faces, 12 edges, and 8 corners.




external image cube.png



external image lightbulb.gif 3-dimensional shapes have three dimensions: length, width, and height.

To practice 2-dimensional shapes.
http://www.numbernut.com/basic/activities/symbol_4card_shapes.shtml

To practice 3-dimensional shapes.

http://www.numbernut.com/basic/activities/symbol_4card_3dshapes.shtml

To practice area.
http://www.shodor.org/interactivate/activities/AreaExplorer/?version=1.6.0_01&browser=MSIE&vendor=Sun_Microsystems_Inc.

To practice comparing area & perimeter.
http://www.shodor.org/interactivate/activities/ShapeExplorer/

To complete an area & perimeter tutorial.
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

To practice using a geoboard.
http://nlvm.usu.edu/en/nav/frames_asid_277_g_1_t_3.html?open=activities

To practice transformations.
http://www.harcourtschool.com/activity/icy_slides_flips_turns/

To complete a tutorial on shapes.
http://www.bbc.co.uk/schools/ks2bitesize/maths/revision_bites/shapes.shtml

To complete another shape tutorial.
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm

To practice using a protractor.
http://www.hittingthetarget.com/hittingthetarget.php

To practice angles.
http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html



Lesson #10



Measurement

external image measurement.gif

Here we will be learning about customary units (American) and metric units.
external image lightbulb.gif Standard customary units of measure for length include inches (in), feet (ft), yards (yd), and miles (mi).

12 inches = 1 foot
3 feet = 1 yard
1 yard = 36 inches
1 mile = 5,280 feet
external image lightbulb.gif How to read a ruler in standard customary units.
The center mark between the numbers is 1/2.


external image half%20inch.gif


The next smallest units on a ruler are fourths.


external image quarter%20inch%204.gif


The next smallest units are eighths.


external image eighth%20of%20inch.gif


The next smallest units are sixteenths.


external image sixteenth%20inch.gif



external image lightbulb.gif The smaller the unit of measurement used, the more accurate the measurement.
external image lightbulb.gif The smaller the unit of measure used to measure an item, the more units it takes to cover the distance. For example: If you measured the ribbon below in inches it would be 36 inches long. If you measured in feet it would be 3 feet long. If you measured in yards it would be 1 yard long. Since the inch is the smallest unit of measure it takes more inches than feet or yards.


external image ribbon.jpg


external image lightbulb.gif Measuring to the nearest unit is like rounding. We measure up to the next bigger unit if the length is halfway or more and down to the smaller unit if the length is less than halfway to the next unit. For example: In picture A below the blue rectangle is closer to 4 inches and in picture B the object is closer to 2 inches.
A
external image quarter%20inch%202.gifB external image quarter%20inch%203.gif







external image lightbulb.gif Metric units of length include millimeters (mm), centimeters (cm), and meters (m).



100 centimeters = 1 meter
10 millimeters = 1 centimeters
1,000 millimeters = 1 meter
external image lightbulb.gif How to read a metric ruler: The larger lines with numbers are centimeters and the smallest lines are millimeters.


external image metric%20ruler.gif


external image lightbulb.gif We measure metric units of length to the nearest cm by rounding. We round up to the next higher cm if the length is 0.5 cm (5mm) or more past the last whole cm. We round down to the smaller cm if the length is less than 0.5 cm (5mm) past that cm. For example: 1.5 cm round up to 2 cm, and 1.4 cm round down to 1 cm.
external image lightbulb.gif Standard customary units of measurement for weight are the ounce (oz) and pound (lb or #). 16 oz = 1 lb
external image lightbulb.gif We measure to the nearest pound the same way we round. If it is halfway or more (8 oz or more), go up to the next pound. If it is less than halfway (7 oz or less), go down to the smaller pound.
external image lightbulb.gif Metric units of measurement for mass are gram (g) and kilogram (kg). 1,000 g = 1 kg
external image lightbulb.gif Capacity is the amount an object can hold.
external image lightbulb.gif Standard customary units of capacity include teaspoon (tsp), tablespoon (tbs), cup (c), pint (p), quart (qt), and gallon (g).



2 cups = 1 pint
2 pints = 1 quarts
4 quarts = 1 gallon
external image lightbulb.gif We can measure with a thermometer if we want to know exactly how hot or cold something is. The units of measure for temperature are degrees and the more degrees there are the hotter the temperature is.
external image lightbulb.gif Fahrenheit measures of temperature are used in this country, while Celsius measures of temperature are used by scientists in this country as well as people internationally.
external image lightbulb.gif Important temperatures to know for Fahrenheit and Celsius are below:


Fahrenheit
Celsius
Freezing Point = 32 degrees F
Freezing Point = 0 degrees C
Comfortable Room Temperature = 70 degrees F
Comfortable Room Temperature = 21 degrees C
Normal Body Temperature = 98.6 degrees F
Normal Body Temperature = 37 degrees C
Boiling Point = 212 degrees F
Boiling Point = 100 degrees C

To practice converting units.
http://www.mathcats.com/explore/convert.html

To see a video on estimating length.
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/2_Estimation_of_Length/index.html

To practice measuring to an inch.
http://www.harcourtschool.com/activity/length_strength4/

To practice measuring to centimeters.
http://www.hbschool.com/activity/length_strength1_centi/

To practice measuring with a ruler.
http://www.thatquiz.org/tq/practice.html?measurement

To practice converting & identify lengths.
http://www.mathcats.com/explore/convert.html

To practice metric measurements.
http://www.teachingmeasures.co.uk/menu.html

To practice measurement & estimation.
http://www.hbschool.com/activity/elab2004/gr5/25.html

To see video on weight and capacity.
http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/6_Weight_and_Capacity/index.html

To practice weighing with scales.
http://www.crickweb.co.uk/assets/resources/flash.php?&file=simplescales2




Lesson #11




Ratio and Probability



external image dice.png


Ratio and Probability: Learn about the chance of an event happening.
external image lightbulb.gif Ratios are one way to compare 2 amounts. Ratios can be written in three forms: as words, as numbers with a colon separating the two amounts, and as fractions. For example: if a class has 14 boys and 15 girls, the ratio of boys to girls is 14 to 15, 14:15, or 14/15.
external image lightbulb.gif
The order of the numbers in the ratio is very important. For example, a class has 14 boys and 15 girls. If we are comparing girls to boys, the ratio is 15 to 14. If we are comparing boys to girls, the ratio is 14 to 15.
external image lightbulb.gif Probability is the chance of something happening. Probability describes whether an event is likely to happen, unlikely to happen, certain to happen, impossible, or more likely, equally likely, or less likely to happen than another event.
external image lightbulb.gif A result of an experiment is called an outcome or event. Possible outcomes are all the possible results or events that might happen.
external image lightbulb.gif Probability of drawing a card: There are 52 cards in a deck so what are the chances of picking a King?

external image king%20of%20spades.jpg
external image king%20of%20clubs%202.jpgexternal image king%20of%20diamonds%202.jpgexternal image king%20of%20hearts%202.jpg







There are 4 Kings in a deck of cards so the probability of drawing a King would be 4 out of 52.

external image lightbulb.gif Probability of flipping a coin and getting Heads or Tails: There are 2 sides to a coin so what is the chance of getting a heads or tails if you flip the a coin?

external image quarter.jpg
external image vermont_quarter.jpg






There is a 1 in 2 chance of getting a head or tail. Remember every time you flip the coin it is always a 1 in 2 chance of getting a head or tail no matter how many times you flip.
external image lightbulb.gif Probability of rolling dice: If you roll 1 di what is the chance of rolling a 2?


external image dice%205.jpg


There are 6 sides to a di so and only 1 side of the di has a two. The chance of rolling a 2 is 1 in 6.
external image lightbulb.gif What if you have 2 dice? What would be the chance of rolling the dice and having the dice equal 5? Remember you can get five with 4 + 1 and 2 + 3.


external image dice%204.gif


Making a chart like the one above is very helpful in this type of problem. There are 36 possible outcomes. 4 of the outcomes will equal 5 so you have a 4 in 36 chance.
external image lightbulb.gif Probability of picking an item: See the examples below --

external image Probability.jpg
external image Probability%202.jpg

external image lightbulb.gif Probabilty of landing on a color on a spinner: What is the probability of landing on yellow when you spin the spinner?


external image spinner%202.gif


There is 1 yellow space on the spinner. There are 4 equal spaces on the spinner. The chance on landing on yellow is 1 in 4.
external image lightbulb.gif You can also use probability to determine if a game is fair or unfair. The teacher gives 1 student spinner A and she gives another student spinner B. She then explains that to win a game the person who spins yellow the most will win. Is this game fair or unfair?
A
external image spinner.gif
B




This game is unfair. The student with spinner A has less of a chance to spin yellow than the student with spinner B. Spinner A has a 1 in 4 chance. Spinner B has a 1 in 3 chance.


To practice probability of rolling dice.
http://nces.ed.gov/nceskids/chances/index.asp


To practice probability of choosing a color.
http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html

To practice probability of tossing a coin.
http://www.mathsonline.co.uk/nonmembers/resource/prob/coins.html

To practice probability using cards.
http://www.e-gfl.org/e-gfl/custom/resources_ftp/client_ftp/teacher/other/spark/playcards/gamelaunch.html

To practice probability using spinners.
http://www.hbschool.com/activity/probability_circus/

To complete a probability tutorial.
http://www.bbc.co.uk/schools/ks2bitesize/maths/revision_bites/probability.shtml

To practice probability of choosing a color.
http://www.bbc.co.uk/schools/ks2bitesize/maths/activities/probability.shtml

To practice probability using spinners.
http://www.mathsonline.co.uk/nonmembers/resource/prob/spinners.html

external image lightbulb.gif Probability Power Point: In Teacher's Files






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I think I'm all through with this Math page.
Click on the numbers to return home then Smiley!