Riley from a young age has a basic understanding of measurement- I have less juice than you do, I have more Blocks than my brother. As her speech and vocabulary develop, measurement words like larger, smaller, longer, shorter, more, and less will become more prevalent. With her brain so active, this is a great time to introduce Riley to comparative measurements for size, amount, and time. Activities like building block towers of different heights, making Piles of different amounts of snacks, and having races across the yard using running, walking, and crawling provide the opportunity to use these words in context. Games like “Mother May I” and “Mrs. Fox What Time Is It” are great for small children to understand distance. Playing with measuring cups in sandboxes or rice bins helps Riley make connections with volume and mass without knowing it.
Riley should have a firm understanding of comparable measurable attributes, such as height, length, amount, and size. At a glance, she should be able to create sentences describing these comparable attributes: Maria is taller than Jimmy; my glass of milk has more than your glass of milk; the school is bigger than my house. At this point, Riley should be introduced to tools used in measuring- a ruler, scale, or measurement cups. It is good practice to measure the length of things that are longer than the tool, so Riley must use problem solving to figure out how to mark where the ruler ends and then use it again to measure the next section. She should know that if the mark does reach the whole number that there are fractional amounts between each whole number. Her measuring skills can also include more abstract units, like time and money. Being able to read a clock is an exciting step in Riley’s independence. She should be encouraged to increase her awareness and responsibility for when she needs to get up, get dressed, leave for dance class, eat dinner, or go to bed. It is important that she understands minutes as fractions of an hour, so she has a strong understanding of the relationship between the two. Riley also has the knowledge to keep track of an allowance as she starts to learn the cost of things and how to count money using 5’s, 10’s, and 25’s. Riley will find lots of daily opportunities to use her measuring skills: filling the dump truck in the sand box, deciding which of her friends is the tallest, discovering which of her pet cats is heavier, knowing what time to come home from a friend’s house or helping Mom measure the ingredients to make cookies.
At the end of 2nd grade, Riley should be able to solve this measurement problem:
60 cents is shared among 4 children, how much do they each get?
Riley has a strong foundation in the concept of measurement, now it’s time to get specific. She should be learning how to use measuring units that remain consistent (inches/feet, centimeters/meters) and how they relate to each other. She is starting to be able to group items into amounts, understanding that a foot is always the same as 12 inches. Riley should be able to tell what unit of measurement is needed for which event: using miles or kilometers to measure the distance a cross country runner runs, or gallons or liters when filling up a tank of gas. Although she doesn’t need to convert one system of measurement to the next between metrics and standard units, Riley should know that meters and feet measure linear distance; gallons and liters measure volume; and pounds and grams measure mass. She will also know that the metric system is based on a Base 10 system while standard units of measure have varying conversion amounts; and she should have knowledge of what those amounts are: i.e. 12 inches = to 1 foot, 100 cm = to 1 meter. Geometric measurement helps to develop a firm understanding of area, perimeter and volume. As she learns and understands formulas for squares, rectangles, and triangles, she will be able to apply them to other simple shapes like rhombuses and parallelograms, as well as some irregular shapes.
At the end of 5th grade, Riley should be able to solve this measurement problem:
Carson needs to purchase 5.6 meters of tape for a project. If each roll of tape contains 80 cm and costs $5, what is the total cost of the tape that Carson must buy?
As Riley’s brain develops, she will be able to process more complex multi-step math problems including ones that involve converting one unit of measurement to another and using several different types of measurement. It is important that Riley be able to explain the process of finding the solution to multi-step word problems, and that she can express them as a formula or equation. Operations should expand to include complex calculations like interest rate. She should also have a firm grasp of negative numbers. Not only can Riley keep track of her allowance and calculate sales prices based on percentages, she can also recognize when she does not have enough money to make a purchase and know how much she needs to save to be able to buy the item. Geometric measurement becomes a primary focus in mathematics at this stage, as measurement becomes intrinsically tied to geometry. Riley will be learning how to calculate the hypotenuse of a triangle using Pythagorean Theorem and what formulas to use to find things like the surface area and volume for shapes like pyramids, spheres, and cylinders. These problems become more complex as Riley is required to apply metric and standard units of measure conversion rates to find the answer.
At the end of 8th grade, Riley should be able to solve this measurement problem:
David currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 3 feet shorter than twice its width. He decides that the perimeter should be 60 feet. Determine the dimensions, in feet, of his new garden.