Statistics, Number Sense, Decimals, and Time

Statistics

In our Statistics unit 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.

  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.

  Line graphs show increases and decreases in a trend. 

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

  A clump is a group of data pieces on the graph.   The clump of the line plot is 0 – 4.

 A hole is a place where there are no data pieces. The holes are at 5, 7, 9, 11, 12 and 15.

 Outliers are pieces of data that are much larger or smaller than the rest of the data. The outliers are 13 or 14.

 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.

 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

 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.

 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.  

 To practice interpreting data.

 To practice line graphs. 

  To learn more about line plots.

 To practice mode, median, mean.  

   To practice reading a graph.

 Number Sense

(Go to bottom of the page for printable Number Sense help notes.)

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

 Numbers 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.

  Each 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

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

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

  Expanded 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.

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

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones

   Place 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.

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

  When 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. 

  We 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.

 To watch a video about place value.  

 To practice naming the value of the digit.

 To practice standard form.   

  To review and practice Expanded Notation.

 To practice word names.  

   To practice less than.    

 To practice more than. 

   To practice estimation.

Decimals 

(Go to the bottom of the page for printable Decimal help notes.)

In our decimal unit we will be learning about the decimal place values tenths, hundredths, and thousandths.  We will also be comparing decimals and finding equivalent decimals.

 A decimal point is a dot that comes between the whole number places and the decimal places in a number.

 All the digits to the right of the decimal point are less than 1 whole.

 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.

 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?

 Tenths are divided into 10 equal pieces.  If all ten pieces are used than we have 1 whole.

  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.

 T housandths 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.

  The standard form of a decimal is written in numbers.  For example: 0.1 

  The word name of a decimal is written in words.  For example: one tenth

  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

  A decimal amount can be modeled on a place value mat.  For example: 

       This number line shows 1.9

 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.

  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. 

  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 

  When you add and subtract decimals make sure to line up the decimals points and then add as usual.  For example:

 Equivalent decimals are decimals that are equal.  For example:   

 To review and practice decimals. 

  To practice adding decimals with number lines.

 To practice identifying decimals.  

 To practice putting decimals on number lines. 

  To practice making the largest decimal.  

 To practice comparing decimals.

 To practice identifying decimals. 

 To practice decimals to the thousandths place.

Time 

(Go to the bottom of the page for printable Time help notes.)

In our time unit we will be learning how to tell time and how to find elapsed time.

 Time 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

 Clocks move in a clockwise movement. 

 a.m. is from 12:00 midnight to 11:59 in the morning.

 p.m. is from 12:00 in the afternoon to 11:59 at night.

 Clocks have a short hand to tell the hour and a long hand to tell the minute.

 Each number on the clock represents 5 minutes.

 Steps to telling time:

1.      Look at the hour hand. The hour hand on the clock below 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.

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.

 Elapsed 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:

1.      The first clock shows 8:00. The second clock shows 1:30.

2.      First I 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.

 To watch a time video. 

 To review and practice telling time.

 To practice telling time to hour & half hour.

 To practice telling time to 5 minutes.

  To practice telling time to nearest minute. 

 To practice elapsed time.

 To practice elapsed time in 1/2 hour.  

  To practice elapsed time word problems.    

Number Sense - Writing Numbers Help Notes (docx file)

Number Sense - Word Names Spelling Help Notes (doc file)

Decimals - Decimal Names Help Notes (docx file)

Time - Telling Time Help Notes (docx file)

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