Measurement & Data
Measurement, Money, and Data with Graphs
Grade 2
- ✓Measure the length of objects using standard units like inches, feet, centimeters, and meters.
- ✓Solve word problems involving dollar bills and coins, using the $ and ¢ symbols appropriately.
- ✓Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
- ✓Draw a picture graph and a bar graph to represent a data set with up to four categories, and solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
Key concepts
When we measure length, we use tools like rulers and measuring tapes. Standard units help everyone understand how long something is. In the United States, we often use inches and feet. An inch is a small unit, and a foot is longer (1 foot = 12 inches). We also use metric units like centimeters and meters. A centimeter is a small unit, and a meter is longer (1 meter = 100 centimeters). When you measure, always start at the '0' mark on your ruler.
Money helps us buy things. We use different coins and dollar bills.\nA penny is worth 1 cent (¢). It's copper colored.\nA nickel is worth 5 cents (¢). It's silver colored and a bit larger than a dime.\nA dime is worth 10 cents (¢). It's silver colored and the smallest coin.\nA quarter is worth 25 cents (¢). It's silver colored and the largest coin.\nA dollar bill is worth 100 cents (¢) or $1.00.\nWhen you count money, it's easiest to start with the coins or bills that have the greatest value.
Clocks help us know what time it is.\nAn analog clock has an hour hand (short hand) and a minute hand (long hand). The hour hand points to the hour, and the minute hand points to the minutes.\nA digital clock shows the time with numbers, like 3:30.\nWe tell time to the nearest five minutes. Each number on the clock face represents 5 minutes when the minute hand points to it (1=5 minutes, 2=10 minutes, 3=15 minutes, and so on).\na.m. means morning (from midnight to noon).\np.m. means afternoon or evening (from noon to midnight).
A picture graph uses pictures or symbols to show data. Each picture usually stands for a certain number of items. It's important to look at the key (or legend) to know what each picture represents. Picture graphs have a title and labels for each category.
A bar graph uses bars to show data. The length or height of each bar shows how many items are in that category. Bar graphs have a title, labels for the categories, and a scale (numbers along one side) to help us read the amount for each bar. Bars can go up and down (vertical) or side to side (horizontal).
Key facts to remember
- 11 foot = 12 inches.
- 21 meter = 100 centimeters.
- 3A penny is 1 cent (¢).
- 4A nickel is 5 cents (¢).
- 5A dime is 10 cents (¢).
- 6A quarter is 25 cents (¢).
- 71 dollar ($1) = 100 cents (¢).
- 8There are 60 minutes in 1 hour.
- 9Graphs need a title, labels, and a key or scale to be understood.
Worked examples
Example 1
Sarah measured her pencil and found it was 7 inches long. Her crayon was 4 inches long. How much longer is her pencil than her crayon?
Answer
Her pencil is 3 inches longer than her crayon.
Remember to include the unit of measurement in your answer.
Example 2
David has 2 quarters, 3 dimes, and 4 pennies. How much money does David have in all?
Answer
David has 84¢.
Always start counting with the coins of highest value to make it easier.
Example 3
A bar graph shows favorite fruits of students. Apples has a bar up to 8, Bananas up to 5, and Oranges up to 6. How many more students prefer apples than bananas?
Answer
3 more students prefer apples than bananas.
Always check the scale on the graph to read the values correctly.
Common mistakes
- ✗Not starting measurement at the '0' mark on a ruler.
- ✗Confusing the values of different coins (e.g., thinking a nickel is 10 cents).
- ✗Misreading the minute hand on an analog clock, especially between numbers (e.g., reading 3:01 as 3:05).
- ✗Forgetting to look at the key or scale on a graph, leading to incorrect interpretations of data.
- ✗Not including the correct unit (inches, cents, minutes) in the final answer.
Exam tips
- ★When measuring, always line up the object with the '0' mark on your ruler or measuring tape.
- ★When counting money, group coins by value and count from largest value to smallest (quarters, then dimes, then nickels, then pennies).
- ★For time, identify the hour hand first, then the minute hand, counting by fives from the 12.
- ★Always read the title, labels, and key/scale of any graph carefully before answering questions about it.
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