The common measures of volume in the U.S. system of measurements are:
The metric system has prefix modifiers that are multiples of 10.
- A kiloliter is 1000 liters
- A hectoliter is 100 liters
- A decaliter is 10 liters
- A liter is the basic unit of volume
- A deciliter is 1/10 liter
- A centiliter is 1/100 liter
- A milliliter is 1/1000 liter
As we move down the units, the next unit is one tenth as large. As we move upward, each unit is 10 times as large. One hundred milliliters, which is 1/10 liter (100/1000=1/10) are larger than one centiliter (1/100th liter).
How to add pounds and ounces
- Add the ounces together.
- If the number of ounces is greater than 16, divide the ounces by 16.
- The quotient is the number of pounds that need to be added to the other pounds.
- The remainder is the number of extra ounces.
- Add the original pounds plus the whole pounds resulting from the addition of the ounces.
Example: Add 5 pounds 8 ounces plus 3 pounds 10 ounces
- Add 8 ounces to 10 ounces:
8 + 10 = 18 ounces - The number of ounces is greater than 16 so divide by 16:
18 ÷ 16 = 1 pound 2 ounces - Add the pounds:
5 + 3 + 1 = 9 pounds - Answer: 9 pounds 2 ounces
Comparing Mass in Grams
The metric system has prefix modifiers that are powers of 10.
- A kilogram is 1000 grams
- A hectogram is 100 grams
- A decagram is 10 grams
- A gram is the basic unit of mass
- A decigram is 1/10 gram
- A centigram is 1/100 gram
- A milligram is 1/1000 gram
The metric system has prefix modifiers that are multiples of 10.
- A kilogram is 1000 grams
- A hectogram is 100 grams
- A decagram is 10 grams
- A gram is the stem unit of mass
- A decigram is 1/10 gram
- A centigram is 1/100 gram
- A milligram is 1/1000 gram
As we move down the units, the next unit is one tenth as heavy. As we move upward, each unit is 10 times as heavy. One hundred milligrams, which is 1/10 gram (100/1000=1/10) are heavier than one centigram (1/100th gram).
The metric system uses the Celsius scale to measure temperature. However, temperatures are still measured on the Fahrenheit scale in the U.S.
Water freezes at 0o Celsius and boils at 100o Celsius which is a difference of 100o. Water freezes at 32o Fahrenheit and boils at 212o Fahrenheit which is a difference of 180o. Therefore each degree on the Fahrenheit scale is equal to 100/180 or 5/9 degrees on the Celsius scale.
How to convert Fahrenheit temperatures to Celsius
- Subtract 32o to adjust for the offset in the Fahrenheit scale.
- Multiply the result by 5/9.
- Example: convert 98.6o Fahrenheit to Celsius.
98.6 - 32 = 66.6
66.6 * 5/9 = 333/9 = 37o C.There is a mental math method to approximate the Fahrenheit to Celsius conversion. The ratio of 5/9 is approximately equal to 0.55555....
How to approximate the conversion of Fahrenheit temperatures to Celsius with mental math.
- Subtract 32o to adjust for the offset in the Fahrenheit scale.
- Divide the Celsius temperature by 2 (multiply by 0.5).
- Take 1/10 of this number (0.5 * 1/10 = 0.05) and add it from the number above.
- Example: convert 98.6o F to Celsius.
98.6 - 32 = 66.6
66.6 * 1/2 = 33.3
33.3 * 1/10 = 3.3
33.3 + 3.3 = 36.6 which is an approximation of the Celsius temperature
The metric system uses the Celsius scale to measure temperature. However, temperatures are still measured on the Fahrenheit scale in the U.S.
Water freezes at 0o Celsius and boils at 100o Celsius which is a difference of 100o. Water freezes at 32o Fahrenheit and boils at 212o Fahrenheit which is a difference of 180o. Therefore each degree on the Celsius scale is equal to 180/100 or 9/5 degrees on the Fahrenheit scale.
How to convert Celsius temperatures to Fahrenheit
- Multiply the Celsius temperature by 9/5.
- Add 32o to adjust for the offset in the Fahrenheit scale.
- Example: convert 37o C to Fahrenheit.
37 * 9/5 = 333/5 = 66.6
66.6 + 32 = 98.6o FThere is a mental math method to convert from Celsius to Fahrenheit. The ratio of 9/5 is equal to 1.8 and 1.8 is equivalent to 2 - 0.2
How to convert Celsius temperatures to Fahrenheit with mental math.
- Double the Celsius temperature (multiply by 2).
- Take 1/10 of this number (2 * 1/10 = 0.2) and subtract it from the number above.
- Add 32o to adjust for the offset in the Fahrenheit scale.
- Example: convert 37o C to Fahrenheit.
37 * 2 = 74
74 * 1/10 = 7.4
74 - 7.4 = 66.6
66.6 + 32 = 98.6o F
The metric system has prefix modifiers that are multiples of 10.
| Prefix | Symbol | Factor Number | Factor Word |
| Tera | T | 1,000,000,000,000 | Trillion |
| Giga | G | 1,000,000,000 | Billion |
| Mega | M | 1,000,000 | Million |
| Kilo | k | 1,000 | Thousand |
| Hecto | h | 100 | Hundred |
| Deca | da | 10 | Ten |
| Deci | d | 0.1 | Tenth |
| Centi | c | 0.01 | Hundredth |
| Milli | m | 0.001 | Thousandth |
| Micro | u | 0.000001 | Millionth |
| Nano | n | 0.000000001 | Billionth |
| Pico | p | 0.000000000001 | Trillionth |
The metric system has prefix modifiers that are multiples of 10.
| Prefix | Symbol | Factor Number | Factor Word |
| Kilo | k | 1,000 | Thousand |
| Hecto | h | 100 | Hundred |
| Deca | da | 10 | Ten |
| Deci | d | 0.1 | Tenth |
| Centi | c | 0.01 | Hundredth |
| Milli | m | 0.001 | Thousandth |
Objectives
National Curriculum
Key Stage 2, Mathematics, Ma2, 3f.
Resources
Teaching activities
Introduction
Ask each child to jot down one division fact corresponding to a times table up to 10 x 10 (for example, 42 ÷ 7 = 6). Stand in a large circle and each takes turns to ask the person to their right their question. Encourage children who are unsure to use the times table square. Time the class and emphasise speed. When everyone has had a go, reveal the time. Tell the children they need to beat this time in the plenary.
Activity
Introduce the online activity to the children. Demonstrate the 'dividing by 9' programme to the class on the whiteboard. Ask several children to come up and solve the division sums. Encourage them to use the 10 x 10 times table square if stuck. Let one group at a time work through the rest of the activity. The other groups can work in pairs, using their whiteboards to set each other division problems corresponding to the 10 x 10 times tables. Once they are able to answer the problems quickly, they can write their divisions as word problems for each other to solve.
Plenary
Play the same circle game as in the introduction. Encourage the children to answer quickly to beat the time. If there is enough time play again and try to beat previous time.
Extension
Children can work through the online quiz.
Homework
Give each child a small 10 x 10 tables grid. Ask each child to choose 2 times tables they are least confident with. Ask them to use the grid to write out all of the multiplication and division sums for those times table.
The Division facts for seven, eight and nine are listed in the following table.
| SEVEN | ||||
| 0 ÷ 7 = 0 | 7 ÷ 7 = 1 | 14 ÷ 7 = 2 | 21 ÷ 7 = 3 | 28 ÷ 7 = 4 |
| 35 ÷ 7 = 5 | 42 ÷ 7 = 6 | 49 ÷ 7 = 7 | 56 ÷ 7 = 8 | 63 ÷ 7 = 9 |
| EIGHT | ||||
| 0 ÷ 8 = 0 | 8 ÷ 8 = 1 | 16 ÷ 8 = 2 | 24 ÷ 8 = 3 | 32 ÷ 8 = 4 |
| 40 ÷ 8 = 5 | 48 ÷ 8 = 6 | 56 ÷ 8 = 7 | 64 ÷ 8 = 8 | 72 ÷ 8 = 9 |
| NINE | ||||
| 0 ÷ 9 = 0 | 9 ÷ 9 = 1 | 18 ÷ 9 = 2 | 27 ÷ 9 = 3 | 36 ÷ 9 = 4 |
| 45 ÷ 9 = 5 | 54 ÷ 9 = 6 | 63 ÷ 9 = 7 | 72 ÷ 9 = 8 | 81 ÷ 9 = 9 |
The Division facts for four, five and six are listed in the following table.
| FOUR | ||||
| 0 ÷ 4 = 0 | 4 ÷ 4 = 1 | 8 ÷ 4 = 2 | 12 ÷ 4 = 3 | 16 ÷ 4 = 4 |
| 20 ÷ 4 = 5 | 24 ÷ 4 = 6 | 28 ÷ 4 = 7 | 32 ÷ 4 = 8 | 36 ÷ 4 = 9 |
| FIVE | ||||
| 0 ÷ 5 = 0 | 5 ÷ 5 = 1 | 10 ÷ 5 = 2 | 15 ÷ 5 = 3 | 20 ÷ 5 = 4 |
| 25 ÷ 5 = 5 | 30 ÷ 5 = 6 | 35 ÷ 5 = 7 | 40 ÷ 5 = 8 | 45 ÷ 5 = 9 |
| SIX | ||||
| 0 ÷ 6 = 0 | 6 ÷ 6 = 1 | 12 ÷ 6 = 2 | 18 ÷ 6 = 3 | 24 ÷ 6 = 4 |
| 30 ÷ 6 = 5 | 36 ÷ 6 = 6 | 42 ÷ 6 = 7 | 48 ÷ 6 = 8 | 54 ÷ 6 = 9 |
Dividing is separating a number into several equal groups.
When we divide 6 by 3 we are separating 6 into 3 equal groups of 2.There are two common ways to write the sign for division.
The number 6 divided by 3 could be written as 6/3 or 6 ÷ 3.Dividing by 0
Numbers cannot be divided by 0 because it is impossible to make 0 groups of a number.
Dividing by 1
Any number divided by 1 equals that number. If you divide by 1 you have one group and so everything is in that group.
Dividing by 2 and 3
The Division facts for two and three are listed in the following table.
| TWO | ||||
| 0 ÷ 2 = 0 | 2 ÷ 2 = 1 | 4 ÷ 2 = 2 | 6 ÷ 2 = 3 | 8 ÷ 2 = 4 |
| 10 ÷ 2 = 5 | 12 ÷ 2 = 6 | 14 ÷ 2 = 7 | 16 ÷ 2 = 8 | 18 ÷ 2 = 9 |
| THREE | ||||
| 0 ÷ 3 = 0 | 3 ÷ 3 = 1 | 6 ÷ 3 = 2 | 9 ÷ 3 = 3 | 12 ÷ 3 = 4 |
| 15 ÷ 3 = 5 | 18 ÷ 3 = 6 | 21 ÷ 3 = 7 | 24 ÷ 3 = 8 | 27 ÷ 3 = 9 |
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