Mathematics Success Level F

Transcription

1 T568 Mathematics Success Level F [OBJECTIVE] The student will determine appropriate units of measurement in the metric and customary measurement systems and complete conversions. [MATERIALS] Student pages S195 S203 Transparencies T583, T585, T587, T589, T591, T593 Paper clips (several per pair) Ruler (1 per pair) *Optional objects that weigh about a gram, a kilogram, an ounce (5 nickels), and a pound (cans of food, etc., work well) [ESSENTIAL QUESTIONS] 1. Why do we use different units of measurement to measure objects? 2. What are the commonly used units of measurement for length and weight in the metric system? 3. What are the commonly used units of measurement for length and weight in the customary system? [WORDS FOR WORD WALL] metric system, customary system, unit, kilometer, km, meter, m, centimeter, cm, millimeter, mm, kilogram, kg, gram, g, mile, mi, yard, yd, foot, ft, inch, in., ton, T, pound, lb, ounce, oz [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Verbal Description, Pictorial Representation, Concrete Representation, Graphic Organizer [WARM-UP] (5 minutes IP, WG, I) S195 (Answers on T582.) Have students turn to S195 in their books to begin the Warm-Up. Students will practice multiplication and division using whole numbers and multiples of 10. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description}

2 Mathematics Success Level F T569 [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] DAY 1: (50 minutes M, GP, IP, WG, I, CP) DAY 2: (50 60 minutes M, GP, IP, WG, I, CP) -Day 1 Units of Measurement Conversion and Appropriate Use Metric System - SOLVE Problem (2 minutes GP, WG) T583, S196 (Answers on T584.) Have students turn to S196 in their books, and place T583 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to determine appropriate units of measurement in the customary and metric systems for length and weight. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE} Metric Measurement Length (10 minutes GP, IP, M, I) T583, S196 (Answers on T584.) 6 minutes M, GP, WG: Use the following activity to complete the steps on S196 with your students. {Concrete Representation, Verbal Description}

3 T570 Mathematics Success Level F MODELING Metric Measurement Length Step 1: Ask students to look at some examples of units of measure as you model. Hold up the smallest finger on your hand as students do the same. Have them look at the thickness of the fingernail. Explain that this is about a millimeter. Explain that the width of the little fingernail is about the length of a centimeter. Continue to model units of measure, as students copy your movements, by extending your right arm straight out from your body and your head turned to the left. Explain that the length from your nose to the fingertips on your right hand is approximately a meter. Point out to students that a meter is longer than a centimeter. Step 2: Have students look at their pencils. Ask them if it would be easier to measure the lengths of their pencils using millimeters (point to the thickness of the little fingernail), centimeters (hold up your pinky finger), or meters (extend your arm and turn your head to model). Students should see that centimeters would be the most appropriate unit. Step 3: Next, ask students if it would be easier to measure the length of the room using centimeters (hold up your pinky finger) or meters (extend your arm and turn your head to model). Students should see that meters would be the more appropriate units. Step 4: Have students model a meter with their arm. Explain that it takes 1,000 meters to equal a kilometer. Ask students what kinds of things might be appropriately measured using kilometers (distance between towns, distance to school from home). Have students record this in the graphic organizer. Step 5: On T583 (S196) model finding objects in the room that could be measured using either millimeters, centimeters, or meters, and think of objects that might be measured with kilometers as an appropriate unit and record. Explain to students that these units are part of the metric system of measurement. 4 minutes IP, WG, I: Have students complete Problems 1 8 at the bottom of S196. Give students 2 minutes to complete the problems and then have them share results with the class. {Verbal Description}

4 Mathematics Success Level F T571 Metric Measurement Conversion with Length (20 minutes GP, IP, M, WG, CP) T585, S197 (Answers on T586.) 12 minutes M, GP: Have students turn to S197 in their books, and place T585 on the overhead. Organize students into pairs and pass out a ruler to each pair. Use the following activity to help students investigate linear conversion within the metric measurement system. {Verbal Description, Concrete Representation, Graphic Organizer} MODELING Metric Measurement Conversion with Length Step 1: Tell students that the metric measurement system is a base 10 system of measurement. Explain that this means that all conversions are based on tens. Have students examine the ruler, find the side with metric units, and compare the millimeter and the centimeter units. Have students compare fingernail thickness to a millimeter and fingernail width to a centimeter. Ask students to find the number of millimeters in 1 centimeter (10). Explain that a meter is 100 centimeters in length. Ask students about how many of the rulers it would take to create a meter (about 3). Make sure students understand that all of these units are based on tens. Explain that there are 10 millimeters in 1 centimeter, 100 centimeters in 1 meter, and 1,000 meters in 1 kilometer. Step 2: Ask students to look at the table at the top of S197 (T585). Point out that it lists the units of measure students have examined. Point out the units millimeter, centimeter, meter, and kilometer. Ask students what these words have in common (meter). Explain that a meter is the benchmark unit to which the other units are compared. Students can think of the word meter as a root or base word with milli-, centi-, and kilo- as prefixes. Step 3: Ask students to underline the word meter in each word and circle the prefixes. Go over the meaning of each of the prefixes and record on T585 (S197). Explain that centi- means one hundredth, because there are 100 centimeters in a meter. Ask students how many millimeters are in a meter. (There are 1,000.) Explain that milli- means one thousandth, because there are 1,000 millimeters in a meter. Record the value of each measurement unit, as students record.

5 T572 Mathematics Success Level F Step 4: Explain to students that each of the units also has an abbreviation. Explain that an abbreviation is a shortened version of a word. Using Dr. for doctor is an example of an abbreviation. Record m for meter, reminding students that this is the benchmark unit. Ask what the abbreviation for centimeter might be (cm). Record. Ask for abbreviations for millimeter (mm) and kilometer (km) and record. Point out that the abbreviations also include the benchmark unit, similar to the words. Kilometer Meter Centimeter Millimeteri km m cm mm 1,000 m 1 m 0.01 m m Step 5: Ask students to put a finger under the word meter on S197 (T585). Ask if the units to the right of the meter are smaller or larger than the meter (smaller). Point out that the value of one of each of the units is recorded as a decimal, which shows a part of a whole. Step 6: Ask students if the units to the left of the meter are smaller or larger than the meter (larger). Point out that the value of one of each of the units is recorded in whole numbers. Step 7: Show students that each of the values contains only 0 s and 1 s. Ask students what happens to the decimal point for a centimeter when compared to a meter (moves two places to the left to show hundredths). Point out that there are 100 centimeters in a meter. Ask students what happens to the decimal point for a millimeter when compared to the meter (moves three places to the left to show thousandths). Point out that there are 1,000 millimeters in a meter. Step 8: Ask students if they would multiply or divide if they were moving from a larger value to a smaller value. Lead them to the answer by having them look at the graphic organizer (multiply). Ask students whether they would multiply or divide if they were moving from a smaller value to a larger value. Lead them to the answer by looking at the graphic organizer (divide).

6 Mathematics Success Level F T573 Step 9: Model how to use the graphic organizer on T585 (S197) for conversions. Have students look at Problem 1. Use the following procedure to model how to solve and record. What is the problem asking us to find? (How many centimeters are in 2 meters?) What measurement unit do we know? (meters) What measurement unit are we looking for? (centimeters) Put your finger on the meter in the graphic organizer and move to the centimeter. Are you moving from larger to smaller units or smaller to larger units? (larger to smaller units) When you move from larger to smaller units, what operation do you use? (multiplication) How many centimeters are in one meter? (100) Multiply 2 by 100 to find the number of centimeters in 2 meters and record the answer. Ask students what happened to the number of zeros in the product when 2 was multiplied by 100 (2 zeros were added). Remind students that they can use mental math when multiplying by values of 10. Problem Means Unit Direction cm = 2 m How many centimeters in 2 meters? Larger to smaller Operation Conversion of 1 unit Multiply 100 cm = 1 m Solution = 200 cm Step 10: Have students look at Problem 2. Use the following procedure to model how to solve and record. What is the problem asking us to find? (How many meters are in 300 centimeters?) What measurement unit do we know? (centimeters) What measurement unit are we looking for? (meters) Put your finger on the centimeter and move to the meter. Did you move from larger to smaller units or smaller to larger units? (smaller to larger units)

7 T574 Mathematics Success Level F When you move from smaller to larger units, what operation do you use? (division) How many centimeters are in one meter? (100) Divide 300 by 100 to find the number of meters in 300 centimeters and record the answer. Ask students what happened to the number of zeros in the quotient when 300 was divided by 100 (2 zeros were removed). Remind students that they can use mental math when dividing with values of minutes CP, WG, IP: Have students complete Problems 3 7 with a partner. Give students 7 minutes to complete the problems and then have them share results with the class. {Verbal Description, Graphic Organizer} Metric Measurement Weight (Units and Conversion) (18 minutes GP, IP, M, WG, CP) T587, S198 (Answers on T588.) 10 minutes M, GP: Have students turn to S198 in their books, and place T587 on the overhead. Use the following activity to help students investigate units and conversion of weight within the metric measurement system. {Verbal Description, Concrete Representation, Graphic Organizer}

8 Mathematics Success Level F T575 MODELING Metric Measurement Weight (Units and Conversion) Step 1: Give student pairs two paper clips. Ask them if they would use this unit of measurement to weigh something light or something heavy. Explain that two paper clips represent a benchmark unit of measure called a gram. Next, either give each pair an object that weighs about a kilogram or pass around an object that weighs about a kilogram, such as a container of ketchup, a jar of mayonnaise, etc. Ask students if they would use this unit of measurement to weigh something light or something heavy. Explain that the object you have provided represents a kilogram. Ask students what kilo- means. (It means 1,000.) Record on T587 as students record on S198. Explain that 1,000 grams equals 1 kilogram. Record the abbreviations and values for kilogram and gram as shown below. Kilogram Gram kg g 1,000 grams 1 gram Step 2: Ask students to think of something that could be weighed using the gram unit of measurement (pencil, paper, eraser, dry erase pen, etc.). Record on T587 as students record on S198. Then ask them to think of objects that might use a kilogram unit of measure (desk, chair, themselves, etc.). Record. Step 3: Model how to use the graphic organizer on T587 (S198) for conversion. Have students look at Problem 1. Use the following procedure to model how to solve and record. What is the problem asking us to find? (How many grams in 1.5 kilograms?) What measurement unit do we know? (kilograms) What measurement unit are we looking for? (grams) Put your finger on the kilogram and move to the gram. Are you moving from larger to smaller units or smaller to larger units? (larger to smaller units) When you move from larger to smaller units, what operation do you use? (multiplication) How many grams are in 1 kilogram? (1,000)

9 T576 Mathematics Success Level F Multiply 1,000 by 1.5 to find the number of grams in 1.5 kilograms and record the answer. Remind students that they can use mental math to find the product. Problem Means Unit Direction g =1.5 kg How many grams in 1.5 kilograms? Larger to smaller Operation Conversion of 1 unit Multiply 1,000 g = 1 kg Solution 1.5 1,000 = 1,500 g 8 minutes IP, WG, CP: Have students complete Problems 2 6 with a partner. Give students 7 minutes to complete the problems and then have students share results with the class. {Verbal Description, Graphic Organizer} Day 2 Customary Measurement Customary Measurement Length (10 minutes GP, IP, M, WG, I) T589, S199 (Answers on T590.) 6 minutes M, GP, WG: Have students turn to S199 in their books, and place T589 on the overhead. Use the following activity to help students investigate linear units of measurement within the customary measurement system. {Verbal Description, Concrete Representation, Graphic Organizer} MODELING Customary Measurement Length Step 1: Ask students to look at some examples of units of measure as you model. Hold up your forefinger and bend, as students do the same. Have them look at the length from one joint to the next joint. Explain that this is about the length of an inch. Continue to model units of measure, as students copy your movement, by looking at your arm from the wrist to the elbow. Explain that this is about the length of one foot. Extend your right arm straight out from your body, facing forward. Explain that the length from your nose to the fingertips on your right hand is approximately a yard. Point out to students that a yard is longer than a foot or inch, and that a foot is longer than an inch.

10 Mathematics Success Level F T577 Step 2: Ask students if it would be most appropriate to measure the length of the room using an inch, foot, or yard unit. Model the units again. Students should see that the yard unit would be a more appropriate unit than the inch or foot unit. Step 3: Next, have students look at the length of a pencil and ask them if it would be easiest to measure the pencil using an inch, foot, or yard unit. Students should see that the inch would be the most appropriate unit. Step 4: Have students show a foot with their arms. Explain that it takes 5,280 feet to equal a mile. Ask students what kinds of things might be appropriately measured using the mile unit (distance between towns, distance to school from home). Step 5: Model finding objects that might be appropriately measured using the inch (length of a paper clip or pencil), foot (height of door or a person), yard (length or width of room), and mile unit and record. Explain to students that these units are part of the customary system of measurement. 4 minutes I, IP, WG: Have students complete Problems 1 6 in the middle of S199. Give students 2 minutes to complete the problems and then have them share results with the class. {Verbal Description) Customary Measurement Conversion with Length (15 minutes GP, IP, M, CP) T589, S199 (Answers on T590.) 5 minutes M, GP, CP: Organize students into pairs and pass out a ruler to each pair. Use the following activity to help students investigate linear conversion within the customary measurement system. {Verbal Description, Concrete Representation, Graphic Organizer} MODELING Customary Measurement Conversion with Length Step 1: Have students examine the ruler, find the side with the customary units, and compare the inch with the length of the ruler, which is a foot. Have students compare the length of the inch on a finger and the length of the arm from wrist to elbow. Ask students how many of the feet (rulers) it would take to create a yard (3). Ask students how many feet (rulers) it would take to equal a mile (5,280).

11 T578 Mathematics Success Level F Step 2: Explain to students that each of the units also has an abbreviation. On T589 (S199), record mi for mile, yd for yard, ft for foot, and in. for inch. Mile Yard Foot Inch mi yd ft in. 5,280 ft 3 ft 12 in. Step 3: Ask students to put a finger on foot. Ask if the units to the right of the foot are larger or smaller than the foot (smaller). Ask students if they would multiply or divide when moving from larger to smaller units (multiply). Step 4: Ask students if the units to the left of the foot are larger or smaller than the foot (larger). Ask students if they would multiply or divide when moving from smaller to larger units (divide). Step 5: Model how to use the graphic organizer on T589 (S199) for conversion. Have students look at Problem 7. Use the following procedure to model how to solve and record. What is the problem asking us to find? (How many feet in 24 inches?) What measurement unit do we know? (inches) What measurement unit are we looking for? (feet) Put your finger on the inch and move to the foot. Are you moving from larger to smaller units or smaller to larger units? (smaller to larger units) When you move from smaller to larger units, what operation do you use? (division) How many inches are in one foot? (12) Divide 24 by 12 to find the number of feet in 24 inches and record the answer. Problem Means Unit Direction ft =24 in. How many feet in 24 inches? Smaller to larger Operation Conversion of 1 unit Divide 12 in. = 1 ft Solution = 2 ft

12 Mathematics Success Level F T minutes IP, WG, CP: Have students complete Problems 8 12 with a partner. Give students 7 minutes to complete the problems and then share results with the class. {Verbal Description} Customary Measurement Weight (Units and Conversion) (18 minutes GP, IP, M, WG, CP) T591, S200 (Answers on T592.) 10 minutes M, GP, WG: Have students turn to S200 in their books, and place T591 on the overhead. Use the following activity to help students investigate weight conversion within the customary measurement system. {Verbal Description, Concrete Representation, Graphic Organizer} MODELING Customary Measurement Conversion with Weight Step 1: Show students a stack of 5 nickels. Ask them if they would use this unit of measurement to weigh something light or something heavy. Explain that the 5 nickels represent approximately an ounce unit. Next, either give each pair an object that weighs about a pound or pass around an object that weighs about a pound (a jar of mayonnaise, half of a two pound bag of flour, etc.) Ask students if they would use this unit of measurement to weigh something light or something heavy. Explain that the object you have provided represents a pound unit of measure. There are 16 ounces in one pound. Record on T591 (S200). Explain that there is one more unit of measurement in the customary system, and it is called the ton. The ton is equal to 2,000 pounds. Record. On the graphic organizer, record the abbreviations. Ton Pound Ounce T lb oz 2,000 pounds 16 ounces Step 2: Ask students to think of something that could be weighed using the ounce unit of measurement (pencil, paper, eraser, dry erase pen, etc.). Record on T591 (S200). Then ask students to think of objects that might use a pound unit of measure (desk, chair, themselves, etc.). Record. Ask students to think of objects that might use a ton unit of measure (car, elephant, etc.) Record.

13 T580 Mathematics Success Level F Step 3: Model how to use the graphic organizer on T591 (S200) for conversion. Have students look at Problem 1. Use the following procedure to model how to solve and record. What is the problem asking us to find? (How many ounces are in 3 pounds?) What measurement unit do we know? (pounds) What measurement unit are we looking for? (ounces) Put your finger on the pound and move to the ounce. Are you moving from larger to smaller units or smaller to larger units? (larger to smaller units) When you move from larger to smaller units, what operation do you use? (multiplication) How many ounces are in 1 pound? (16) Multiply 3 by 16 to find the number of ounces in 3 pounds and record the answer. Problem Means Unit Direction oz =3 lb How many ounces in 3 pounds? Larger to smaller Operation Conversion of 1 unit Multiply 1 lb = 16 oz Solution 3 16 = 48 oz 8 minutes IP, WG, CP: Have students complete Problems 2 7 with a partner. Give students 7 minutes to complete the problems and then have them share results with the class. {Verbal Description} SOLVE Problem (5 minutes GP, WG) T593, S201 (Answers on T594.) Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (Students will use what they have learned about linear conversion within the metric system.) {SOLVE, Verbal Description}

14 Mathematics Success Level F T581 If time permits (10 minutes IP, I) S202 (Answers on T595.) Have students complete Problems 1 10 to practice conversion within the metric or customary system for length and weight. {Verbal Description, Graphic Organizer} [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. Why do we use different units of measurement to measure objects? (to appropriately measure lighter and/or heavier objects) What are the commonly used units of measurement for length and weight in the metric system? (Length: km, m, cm, mm Weight: kg, g) What are the commonly used units of measurement for length and weight in the customary system? (Length: mi, yd, ft, in. Weight: T, lb, oz) [HOMEWORK] Assign S203 for homework. (Answers on T596.) [QUIZ ANSWERS] T597 The quiz can be used at any time as extra homework or to see how students did on conversion within the metric or customary systems for length and weight.