Measurement: Volume, Weight, Mass Day 1: Volume in Customary Units SOL: 4.8 The student will a) estimate and measure liquid volume and describe results in US Customary units Objectives: •
•
•
The students will determine an appropriate unit of measure (cups, pints, quarts, gallons) to use when measuring liquid volume in U.S. Customary units. The students will estimate the liquid volume of containers in U.S. Customary units of measure to the nearest cup, pint, quart, and gallon. The students will measure the liquid volume of everyday objects in U.S. Customary units, including cups, pints, quarts, and gallons, and record the volume including the appropriate unit of measure (e.g., 24 gallons). Learning Target: Materials: Rice and water Measuring cups and Containers Laptop and Projector Copies of Big G Gallon King drawing for students’ math notebooks Engage and Hook: I will estimate and measure liquid volume in US Customary units. King Gallon video https://www.youtube.com/watch?v=BHOrKVlgRec Explain and Model: Today and tomorrow, we are going to talk about liquid volume. What is liquid volume? It is the amount of space that a liquid takes up. One reason why it is important to measure volume is so that we know how much vegetable oil to add to cake batter. Not only is it important to use measurement, but it is also important to measure accurately. Inaccurate measurements can lead to spoiled cakes or botched science experiments! When we measure liquid, we can use metric units or US Customary units. The units of measurement we saw in the video were US Customary units, which we are going to use today and tomorrow. What were some of the units that the video mentioned? Cups, pints, quarts, and gallons. Let’s start by putting these in order from least capacity to greatest capacity. Capacity means the “maximum amount that something can contain” (google). What holds the least amount of liquid? A cup. What hold the most amount of liquid? A gallon. Now which holds more, pints or quarts? How do you know? If one quart queen is equal to two pints, one quart is larger than one pint. Write the measurement units in order from least to greatest capacity on the board, and match a measuring cup or jar to each. Now one of the real-­‐life applications of measuring volume comes when you are shopping for glasses. Which glass do you think has the bigger capacity, or do you think they are equal? Who can tell me what I mean by “bigger capacity”? Which holds more water? Give tables 30 seconds to turn and talk, then solicit guesses. Show students how to measure (there are two ways, pouring from the container whose capacity you wish to measure, or pouring from the measuring utensil), and follow through. The taller glass has a capacity of 2 cups while the capacity of the shorter glass is 1.5 cups. Explore and Apply: Display the Big G Gallon King on the whiteboard. Have students work in pairs to answer the question, “What is the most appropriate unit of measurement for…” a test tube-­‐like container topped with rice, a tuna can filled with rice, soup can topped with rice, and a container for a lunch box topped with rice. Students submit their guesses as to what unit of measurement should be used to measure the above quantities after one minute. After sharing ideas, students estimate the volume of the above items. They may hold the measuring cups and compare them to the containers of rice to help them visualize and estimate. Have students estimate the volume of each rice-­‐filled item, in pairs, with one minute per item. At the end of the five rounds, students share estimations. Then, demonstrate measuring the first item using the unit of measurement proposed. Explain aloud that you are carefully pouring the contents of the container into the measuring cup or container that equals 1 pint, 1 quart, or 1 gallon. When the amount surpasses the 1 line or the fills the capacity of the comparison measurement tool, pour the rice into a spare tray temporarily. After measuring the remainder and adding that to the original whole, write the value as a fraction or decimal. Students write the actual measurement, in fraction or decimal form, next to their estimate. Students work in pairs to help their partner measure accurately and announce measurement to the team after one minute. Evaluate and Close: Students write the unit of measurement that would be most reasonable to use if measuring the capacity of the bucket of rice, and estimate its capacity on an exit ticket. Differentiation: Groups C and D: measure each item as a group, with students taking turns pouring the contents of the container into the chosen measuring tool. Homework: http://www.superteacherworksheets.com/measurement/gallonbot-­‐
questions_TWBQW.pdf Day 2: Weight: Customary Measurement SOL: 4.6 The student will a) estimate and measure weight/mass and describe the results in US Customary and metric units as appropriate Objective: The students will measure weight to the nearest ounce and pound and describe the results in US Customary units. Learning Target: Materials: Engage and Hook: I will measure weight to the nearest ounce and pound. Scale Familiar objects to estimate and measure Measurement recording sheet Today we begin to discuss weight. In the US Customary system for measuring weight, we have three units: ounce, pound, and ton. Which is the least unit of measure? Ounce. We can write ounce spelled out, or with the abbreviation oz. I heard someone pronounce oz like the Wizard of Oz, but when we see oz behind a number, we say “ounces”. Can you think of any objects you’ve encountered whose weight is described in ounces? Think about going to the grocery store. You might look at the bottom left corner of a box of cereal to find its weight. You might want to buy the cereal that has the most weight for the least price. Here is a box of Honey Nut Cheerios whose contents weigh 1 lb 5.6 oz. There are 16 ounces in 1 pound. That is, an object weighing 16 ounces weighs 1 pound. So the number of ounces we have is 16 + 5.6 oz, or 21.6 oz. That being said, what is the next greatest unit of measure, a pound or a ton? A pound. Can you think of anything whose weight is described in pounds? (Ex: human, weights that you lift, backpacks when full, etc.). When we write pounds, we use the abbreviation lb. That is because lb stands for the Roman phrase libre pondo, which meant “a pound by weight.” There are 2,000 pounds in one ton. Have you ever encountered an object weighing more than 2,000 pounds? Have you seen road signs on bridges with weight restrictions? Some bridges can only support vehicles weighing less than a few tons. Explain and Model: Today you are going to have the opportunity to weigh some familiar items using scales! I’ll demonstrate with a calculator first. I’m going to estimate the weight of this calculator. I’ll start with comparing it to a pound. Do you think that this calculator weighs less than or more than a pound? Less than. Would you think it is less than or more than half a pound? Because I really don’t know what half a pound feels like, but this calculator is very light. I’ll estimate the weight of this calculator to be less than ½ a pound. ½ a pound is 8 oz, so I think the calculator weighs less than 8 oz. To measure an object’s weight to the nearest ounce, you must first ensure that the needle is at the 0 oz line. If your needle is already at more than 0 oz, take note of that and subtract that value from your weight to get an accurate measurement. Now, place the item on the plate of the scale. Now, read the measurement by counting the number of benchmarks greater than 0 that your needle matches to. The calculator weighs __ oz. I just measured to the nearest ounce! Model measuring the object to the nearest pound. With an object weighing less than a pound, your final answer can be one of two options. 0 pounds or 1 pound. Would our __-­‐oz calculator, measured to the nearest pound, be 0 pounds or 1 pound? Why? Explore and Apply: Today you are going to measure objects to the nearest ounce and pound. Students go to stations in groups of five. They measure the weight of light classroom objects and record measurements on Measurement Recording Sheet. Evaluate and Close: Students estimate the weight of one cup of uncooked rice, and I weigh it before the class before the end of class. I model subtracting the weight of the measuring cup itself. Students put a check or x by their estimation and write the measured weight on the bottom of their Measurement Recording Sheet. Day 3: Metric Mass Measurement SOL: 4.6 The students will a) estimate and measure weight/mass and describe the results in US Customary and metric units as appropriate Objective: The students will estimate and measure mass in metric units. Learning Target: I will estimate and measure mass in metric units. Materials: Balance scales with gram cubes Kitchen scales Engage and Hook: In whole group, explain the difference between mass and weight: “Mass is the amount of matter in an object. Weight is determined by
the pull of gravity on the mass of an object. The mass of an object
remains the same regardless of its location. The weight of an object
changes depending on the gravitational pull at its location. In
everyday life, most people are actually interested in determining an
object’s mass, although they use the term weight (e.g., “How much
does it weigh?” versus “What is its mass?”).” (Curriculum
Framework)
Explain and Model: In whole group, model how to measure the mass of an object on each scale, emphasizing the benchmarks we look at on the kitchen scale (on the outside of the circle). Think aloud about how many kg are equivalent to the grams of the object, and vice versa to provide a basis for identifying equivalent measurements. Explore and Apply: At the table, students measure the mass of 4-­‐5 objects in grams and kg, using the balance scale with objects with a mass of under 1 kg and the kitchen scale with objects with a mass of more than 1 kg. Students write the mass of the object in both mm and kg. Evaluate and Close: Have students check their measurements with peers and teacher. No exit card today. Day 4: Customary Equivalent Measurements in Volume SOL: 4.8 The student will a) estimate and measure liquid volume and describe results in US Customary units b) identify equivalent measurements between units within the US Customary system (cups, pints, quarts, and gallons) Objective: •
The students will identify equivalent measures of volume between units within the U.S. Customary system. Learning Target: Materials: I will identify equivalent measures of volume between cups, pints, quarts, and gallons. Cup, Pint, Quart, Gallon measuring cups Containers of rice from Monday White board and chalkboard Students’ Math Notebooks Engage and Hook: Do a silent demonstration before the class and have students take notes during it in their math notebooks. Have the following equivalencies on the board: 2 cups = 1 pint; 2 pints = 1 quart; 2 quarts = 1 gallon. Also have the Big G Gallon King picture on the board. During the demonstration, pour two cups of rice into an empty pint container, that now-­‐full pint container and one already full into a quart container, and that now-­‐full quart container plus three already full into a gallon container. Split students into groups where students can share what they saw (that one pint can hold two cups of rice or “water”, one quart can hold two pints of rice, and one gallon can hold four quarts of rice). Explain and Model: Students share what they saw. Write the equivalents that were on the chalk board on your whiteboard and verbalize them, explaining that the capacity of one pint is equal to the capacity of two cups, so a container that can hold one pint of liquid can hold exactly two cups of liquid, etc. Tell students that these basic equivalents allow us to figure out how many cups of liquid one quart can hold, for example. In fact, we are going to find that out now. We can use a number of strategies to figure out this conversion. We can use our reasoning skills to think through it and say, if one quart can hold two pints, and each pint can hold two cups, there are ___ cups in one quart. We can also draw our Big G Gallon King and count the number of cups in one quart. Tell them that if they ever get flustered on a test and can’t do the math in their heads, they can draw the Big G with 4 Q’s, 8 P’s, and 16 C’s. We can also test it out with our measuring containers and rice. Explore and Apply: Ask students to think through how many cups of rice one quart can hold. After everyone has had the chance to take an educated guess and explain their reasoning (which may include reference to the Big G Gallon King), ask students to pour one scoop of rice into the quart measuring jar one at a time until we fill the quart jar. Write the resulting equivalence on the table or whiteboard and have students write 4 cups = 1 quart in their math notebooks. Ask students whether we can write the equivalence this way: 1 quart = 4 cups. Ask students how many cups of rice one gallon can hold. Prompt them to think about how many cups one quart can hold and how many quarts one gallon can hold. Encourage students to draw their Big G Gallon King and count the C’s in it if they have difficulty reasoning through the equivalence. After students share their guess and reasoning, have students pour one cup of rice into the gallon container each. Ask students, now that we have tested it, how many cups can one gallon hold? 16. Have students write 16 cups = 1 quart in their math notebooks. Now we are going to think about bigger quantities of liquid. Say that the recipe for a lot of ice cream calls for 6 pints of milk. Well, we don’t have pint measuring containers. We only have cups. Go through the above process: 1) Have students think it through using reasoning and/or the big G. 2) Have students test it. 3) Write the equivalence on the board and students write it in their math notebooks. Now what if we only had quart containers, and no cups? How many quarts of milk would we add to the mixing vat to equal 6 pints? Go through steps 1-­‐3. 2.5 Q = 6 Pints. Evaluate and Close: Say that we were making slushies for the whole class. We had our giant mixing vat, lots of shaved ice, and now our last step is to add the syrup. The recipe calls for 8 quarts of syrup, but we only have an empty milk jug with a capacity of 1 gallon. How many gallons of syrup do we need to add to our shaved ice to equal 8 quarts? Students may think through it and write the Gallon man, since those are their options on the SOL. Homework: http://www.superteacherworksheets.com/measurement/capacity-­‐
easy_TWBMN.pdf Day 5: Customary Equivalent Measurements in Weight SOL: 4.6 The student will b) identify equivalent measurements between units within the US Customary system (ounces, pounds, & tons) and between units in the metric system (g and kg) Objective: The students will identify equivalent measurements of weight between units in the US Customary system (ounces, pounds, and tons) Learning Target: Materials: Engage and Hook: I will identify equivalent measurements of weight between ounces, pounds, and tons. Math notebooks Calculator Today we get to use our reasoning skills and calculators to think about finding equivalent measurements of weight in the US Customary system. Let’s start by taking some notes in our math notebooks. Yesterday we started talking about different units of measurement in the US Customary system, and there were three. What were they? Let’s put them in order from least weight to greatest. What would that be? Ounces, Pounds, Tons. What are the abbreviations for ounces and pounds? Oz and lb. How many ounces are equivalent to one pound? 16 ounces = 1 pound. Write that on the board and have students write it in their notebooks. Explain and Model: Let’s start with an example. If I have a big 18-­‐wheeler truck whose weight equals two tons when it’s full of cargo, how many pounds does it weigh? Write: 2 tons = ? pounds on the board and have students copy it in their notebooks. How many pounds are in one ton? 2000. Write: 1 ton = 2000 pounds underneath the first line. Teach students to cross-­‐multiply: 2000x2=4000. The 18-­‐wheeler truck weighs 4000 pounds. Let’s do another problem in which we divide instead of multiply. Say that a big rope toy for a dog two pounds. How many ounces does it weigh? Explore and Apply: Use the gradual release model to work through five of the six problems that involve multiplication and five of the six problems that involve division. Evaluate and Close: Students complete the sixth problem with multiplication and division independently as an exit ticket. Day 6: Equivalent Measurements in Metric Mass SOL: 4.6 The students will b) identify equivalent measurement between units within the US Customary system and within the metric system (grams and kilograms) Objective: The students will identify equivalent measurement between units within the metric system (grams and kilograms) Learning Target: I will find equivalent measurements between units in the metric system (g and kg) Materials: Math Notebooks Notes Worksheet Engage and Hook: In whole group, explain that today we are finding equivalent measurements of mass between units in the metric system. In the metric system, we have 2 units of measure. What are they? Grams and kilograms. How many grams are equivalent to 1 kg? 1,000. Explain and Model: When we convert from grams to kilograms or from kg to g, we will write the equivalence fact 1,000 g = 1 kg under the problem, every time. That’s our first step. What is the first step in an equivalence problem? Write the equivalence fact. And when we write this equivalence fact, we write each unit right underneath its partner. For example (WRITE ON BOARD), when converting from 2 kg to __ grams, we write under it 1 kg = 1,000 grams. The kg are lined up with each other, and the g are lined up with each other. Then what do we do? Think back to last Friday, when we converted among units within the US Customary system for weight: we’re either going to cross multiply or divide. When we are converting from a larger unit of measure (kg) to a smaller unit of measure (g), we cross multiply. So what operation do we use when converting from kg to g? Multiply. Complete that example: 2,000g What if we are converting from g to kg? We divide. Complete the example 100g=___kg on the board. Explore and Apply: At the table, students complete the worksheet as gradual release model. Do the first two as a group, then the next two in partners, and the last individually. FOR GROUPS C AND D. Do the first three sets together, then one set as partners, then one set individually. Evaluate and Close: What do you notice about multiplying and dividing by 1,000? Look at the number of grams or kilograms you started out with and look at the equivalent measure you found. Let’s take the second one for example: 2.5 kg = 2,500 grams. What do you notice about these numbers? The first two digits are the same, and there are two zeros after the 25 in 25 grams. Lead students to see that when converting from kg to g, you simply move the decimal point three to the left. You must show students that for problems without an explicit decimal point, such as number one (8 kg = 8,000 g), any whole number can become a decimal. The decimal point will be after the ones place, and there are 0s in all of the place values after it. So when converting from kg to g, simply move the decimal point three to the right.