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## Measurement and Data

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**Measurement and Data**Everyday Mathematics Unit 10 Mr. Brumfield Lawnton Elementary**Table of Contents**10.1 Review: Length 10.2 Volume 10.3 Exploring Volume 10.4 Weight 10.5 Weight and Volume 10.6 Capacity 10.7 The Mean and the Median 10.8 Calculating the Mean 10.9 Calculator Memory 10.10 Frequency Distributions 10.11 Coordinate Grids 10.12 Unit Review and Assessment**Lesson 10.1**Review: Length Why units and tools to we use to measure?**Mental Math**5 x 7 3 x 3 5 x 5 4 x 9 9 x 7 9 x 9 40 (20s) 30 (70s) 20 (100s) 60 (20s) 40 (80s)**Math Message**The inch is a unit of length. List as many other units of length as you can.**Metric Units**U.S. Customary Units Categorizing Units of Measurement**Finding Measurement Equivalencies**Metric System 1 Kilometer meters 1 Meter • decimeters 1 Meter centimeters 1 Meter millimeters 1 Decimeter centimeters 1 Centimeter millimeters**Finding Measurement Equivalencies**U.S. Customary Units 1 Mile yards 1 Mile • feet 1 Yard feet 1 Yard inches 1 Foot inches**How would you categorize these tools?**Car odometer Category:**Thinking About Measurement**Would it make sense to measure the distance between two cities with a yardstick? How could you measure the circumference of (distance around) the lid of a jar? How would you measure the diameter of a ball? How would you estimate the height of a three story building?**Renaming Measurements**Is 18 inches more or less than a foot? What fraction of 1 foot is 6 inches? 2 yards is equal to how many feet? 2 feet is equal to how many inches? Give another name for 2 feet 3 inches: Give another name for 5 feet:**Independent Practice**Math Journal Page 246 Practice measuring in centimeters and inches, renaming measurements, and finding the areas of rectangles. Remember to begin measuring at the 0 mark. Math Boxes on page 248**Group Work**Math Journal Page 247 With a partner you will read about the layers of the earth. You will need to use the distance key and the information in the reading to help you answer the four questions.**Lesson 10.2**Volume What is volume and how is it measured?**Mental Math**Write three and nine hundredths. Underline the digit in the tenths place. Four and fifty hundredths Circle the digit in the hundredths place. Underline the ones. Seventeen and ninety-three hundredths Underline the ones digit. Put an X through the tenths.**Introducing the Volume of a Rectangular Prism**This arrow is showing: ___________________ These arrows are showing: ___________________ Bases of a Prism Remember that bases are any two pairs of opposite faces. The bases are rectangular and parallel and have the same area. Height of a Prism The height of a prism is the distance between the two opposite bases.**Group Work**Math Journal Page 249 Part One Only Each student will need 10 cm cubes. We will break into groups of 4 students. Each group will get a copy of math masters 166. Each student is responsible for cutting out and taping a rectangular prism (A, B, C, or D). Discuss the prisms from your group and estimate how many cubes you think it will take to fill each of the rectangular prisms. How will you find out how many cubes would fill the prisms?**Group Work Follow Up**Math Journal Page 249 Part One What do you notice about the cubes in the rectangular prisms? Is there an algorithm we could use to easily find the number of cubes in a prism? The number of cubes needed to fill a box is the volume of the box. The algorithm for volume is: Area of Base X Height**Finding Volume Practice**10 7 4 2 3 3 5 6 4 Area of Base:______ Height: ___________ Volume: __________ Area of Base:______ Height: ___________ Volume: __________ Area of Base:______ Height: ___________ Volume: __________ Is it possible for two different size rectangular prisms to have the same volume?**Independent Practice**Complete part two of math journal page 249. You will be finding the volume of three different rectangular prisms. Remember: area of base X height When you have finished, complete the multiplication problems on math journal page 250. (You can use either partial products or the lattice method)**Math Boxes**Complete the review math boxes on page 252 of your math journal.**Lesson 10.3**Exploring Volume Can rectangular prisms of different sizes have the same volume?**Mental Math Riddles**If you take ½ of me, I will be an odd number. I am less than 20. One of my factors is 5. Who am I? Solve the Problem**Mental Math Riddles**If you double me, I will be a 3-digit number The sum of my digits is 6 2, 3, 4, 5, and 6 are some of my factors Who am I? Solve the Problem**Mental Math Riddles**1/3 of me is equal to ½ of 16 Who am I? Solve the Problem**Math Message**A rectangular prism is made of 45 cubes The base has 15 cubes How many layers of cubes does the prism have? What operation is needed to solve this problem? What information do you have? What information is needed? Fact Triangle**Reviewing the Volume of a Rectangular Prism**This arrow is showing: ___________________ These arrows are showing: ___________________ Bases of a Prism Remember that bases are any two pairs of opposite faces. The bases are rectangular and parallel and have the same area. Height of a Prism The height of a prism is the distance between the two opposite bases. Volume of a Rectangular Prism Multiply the area of the base X the height of the prism**Practicing Finding Volume Review**12 5 4 2 2 3 5 9 6 Area of Base:______ Height: ___________ Volume: __________ Area of Base:______ Height: ___________ Volume: __________ Area of Base:______ Height: ___________ Volume: __________ Is it possible for two different size rectangular prisms to have the same volume?**Exploring Volume**You and your assigned partner will be given 36 cubes which will be your volume. You need to use these blocks to build different bases and heights with the same volume (36 cubic units). Record your findings on math masters 168**Exit Slip: Volume**What have we learned about volume today?**Math Boxes**Complete the review math boxes on page 254 of your math journal.**Lesson 10.4**Weight What are the different tools we can use to measure weight?**Mental Math**Louise had 10 quarters. She gave 2/5 of her quarters to her brothers. How many did she give him? Number Model: _________________ Answer: _______________ Rick’s dad made two apple pies. Six people shared the pies equally and finished them. What fraction of a pie did each person get? Number Model: _________________ Answer: _______________**Math Message**Measuring Weight What do we already know about weight? What units of measurement can you list?**Metric Units**U.S. Customary Units Categorizing Units of Weight**Examining Kinds of Scales**Let’s look at different types of scales found in your SRB, on pages 147 and 148. There are two things we need to know about scales. Capacity of a Scale: the weight a scale can measure. Precision: the size of the unit of measurement. The smaller the unit the more precise the scale.**Group Work: Exploring Scales**You will be working with a partner to complete math journal page 255. You will be brainstorming objects that can be measured or weighed by the different scales that are categorized. When you have finished you may complete math journal pages 256 and 257 independently. You will be working with weight on these pages also.**Math Boxes**Complete the review math boxes on page 258 of your math journal.**Lesson 10.5**Weight and Volume How can we organize objects by weight and volume?**Mental Math**49 candies shared by 5 friends. How many candies for each friend? Answer: __________________________ 6 boxes of crayons with 8 crayons in a box. How many crayons altogether? Answer:________________________ 9 tables with 4 children at each table. How many children? Answer: ___________________________ 300 pennies shared by 10 children. How many pennies per child? Answer: __________________________**Examining 4 Objects**I will be displaying four objects. You need to evaluate them and estimate the order of the items by weight. Use part one of math journal page 251. Then estimate and rank the order of items by volume, using part two of the same page.**Discussing your Estimates**Take a minute to discuss your predictions with your partner. Why did you rank certain objects as heavier or lighter? How did you rank your volume? Explain your thinking.**Conducting the Volume Experiment**We are going to test the volumes of our four objects using containers and water. We will be measuring how much water is displaced from the container after each object is inserted. The more water displaced, the greater the volume of the object.**Discussing the Experiment**How you would explain the relationship you noticed? Can you name two objects for which the heavier of the two also has a greater volume? Can you name two objects for which the heavier of the two has the smaller volume?**Independent Work**Complete the parentheses puzzles on the bottom of page 251. Remember that the parentheses tell you what operation to do first. Complete the review math boxes on page 259 of your math journal.**Lesson 10.6**Capacity What is the capacity of a container?**Mental Math**We are going to compare fractions to ½. You need to mark whether the fraction is greater, less than, or equal to ½. 1/2 1/4 7/8 1/2 2/3 1/2 3/6 1/2 How did you solve the comparison? 1/2 3/5 1/2 5/8**Math Message**The pint is a unit of measure for liquids such as milk and juice. List as many other units as you can that are used to measure liquids.