Explorations Exploring Data, Shapes, and Base-10 Blocks Objectives To measure children s heights; to provide experiences making a bar graph; to guide the exploration of 2-dimensional shapes; and to develop familiarity with base-10 blocks. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Key Concepts and Skills Count and record the number of flats, longs, and cubes. [Number and Numeration Goal 3] Create a line plot and a bar graph to organize data. [Data and Chance Goal 1] Answer questions about data collected using a bar graph; find typical value in a data set. [Data and Chance Goal 2] Estimate and measure height to the nearest inch. [Measurement and Reference Frames Goal 1] Create plane shapes and designs on a geoboard. [Geometry Goal 1] Key Activities Exploration A: Children measure their heights and help make a line plot as the measurements are taken. They use the data in the line plot to create a bar graph. Exploration B: Children make shapes and designs on a geoboard and record them on dot paper. Exploration C: Children build structures with base-10 blocks and record how many of each type of block they use. Key Vocabulary typical bar graph Materials Home Link 4 6 Exploration A: Per group: Math Journal 1, p. 6 tape measure a book Class Data Pad stick-on notes Exploration B: Per group: Math Masters, p. 315 or 316 geoboards rubber bands (colored, if possible) Exploration C: Per group: Math Masters, p. 102 base-10 blocks Ongoing Learning & Practice Using 8 and Pennies in Two-Fisted Penny Addition Math Masters, p. 5 pennies Math Boxes 4 7 Math Journal 1, p. 70 Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 4. [Operations and Computation Goal 1] Home Link 4 7 Math Masters, p. 103 Differentiation Options ENRICHMENT Estimating Length on a Geoboard Math Masters, p. 104 per partnership: geoboard, rubber bands, 6-inch ruler EXTRA PRACTICE Minute Math + Minute Math +, pp. 18, 53, and 58 Advance Preparation For Exploration B, make copies of the geoboard dot paper that matches your geoboards by using Math Masters, page 315 or 316. For Exploration C, make copies of Math Masters, page 102. Cut them in half. Teacher s Reference Manual, Grades 1 3 pp. 11 125, 151, 152 Lesson 4 7 307
Getting Started Mental Math and Reflexes Tell the following number stories. Have children solve them any way they can, sharing their solution strategies. Encourage children having difficulty to draw pictures or doodles, count on the number line or number grid, or use cubes or coins to model the problems. You may want to ask children what information in the last two problems is not needed to solve the problems. Ricardo bought 12 red apples. At the end of the week, 10 apples had been eaten. How many apples were left? 2 apples Antonia and Kris went to the zoo. They saw 6 monkeys, 7 parakeets, and 4 parrots. How many birds did they see? 11 birds Miranda made 2 pizzas for 5 of her friends. Miranda put 21 slices of pepperoni on the first pizza and 16 slices of pepperoni on the second pizza. How many more slices of pepperoni were on the first pizza than on the second? 5 slices of pepperoni Math Message Estimate about how many feet tall most of the first graders in our class are. Home Link 4 6 Follow-Up Ask volunteers to describe and discuss the use of the measuring tools they found at home. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Have children share their estimates. Use a tape measure or yardstick to show the estimates. Mention that another name for the height of most first graders in the class is the typical height of a first grader in the class. To support English language learners, discuss the meaning of typical and review its pronunciation. Ask children how they would check their estimates. Here are a few possibilities: Measure the heights of all first graders. Then: choose the most frequent height. choose a number to which many heights seem to be close. choose one of the heights from the middle if the heights are lined up in order. measure just one child. (In this case, talk briefly about how one would choose whom to measure.) You may want to extend the discussion by having children estimate how many inches tall a typical first grader is. ELL 308 Unit 4 Measurement and Basic Facts
Student Page Exploration A: Measuring Children s Heights and Making a Line Plot (Math Journal 1, p. 6) SMALL-GROUP Attach a tape measure, showing inches, to the wall. Have a volunteer stand straight, with head level, against the tape measure. Demonstrate how to measure the child s height. Show children how to use a book held against the wall on top of the head to get an accurate measurement. Explain that the measurement is read at the bottom of the book. Have children record today s date on the journal page. Work with children to measure the height of each child in each group. When the group agrees on the height of a child, the child records his or her height in the first section of the journal page and on a stick-on note. Draw a horizontal line on the Class Data Pad. Number the line from 38 to 52 or use other numbers that are appropriate for your class and label the line Inches Tall. Make a line plot by having children attach their stick-on notes above their heights. 1. Today s date is. My height is inches. Answers vary. Measuring Height 2. This is a bar graph. It shows the heights of children in my class. First-Grade Heights 7 6 5 Math Journal 1, p. 6 Time 4 3 2 Number of Children 1 Inches Tall 3. The typical height for first graders in my class is about inches. NOTE Children will measure their heights again in Unit. Save the stick-on notes so the data can be used in Lesson -5. NOTE For practice constructing object graphs, go to www.everydaymathonline.com. Teaching Aid Master Exploration B: Exploring Shapes on the Geoboard (Math Masters, p. 315 or 316) SMALL-GROUP Geoboard Dot Paper (5 5) 1. 2. Children make different shapes and designs on the geoboard using (colored) rubber bands. They then copy their favorite designs onto geoboard dot paper. 3. 4. 5. 6. Math Masters, p. 315 Lesson 4 7 30
Teaching Master Building with Base-10 Blocks Exploration C: Building Structures with Base-10 Blocks (Math Masters, p. 102) SMALL-GROUP Flats Longs Cubes 1. 2 8 4 2. 3. 4. Children build structures with base-10 blocks to become familiar with the names, shapes, and sizes of these manipulatives. Children record how many flats, longs, and cubes they use for each structure. Building with Base-10 Blocks NOTE Provide enough base-10 blocks for each child to have 25 cubes (ones), 12 longs (tens), and 2 flats (hundreds). Flats Longs Cubes 1. 2 8 4 2. 3. 4. Math Masters, p. 102 NOTE The horizontal axis is a reference line for listing the different heights. The vertical axis is a reference line for the number of children who are a certain height. NOTE Everyday Mathematics does not draw a distinction between histograms and bar graphs. For a discussion on how some people contrast them, see Section 12.2.3: Organizing and Displaying Data in the Teacher s Reference Manual. NOTE To find a typical height in another way, first list the heights in order and then find the height in the middle of the list. This description of a data set is called the median. Another way to describe a set of data is to find the most frequent value in the set of data. This is called the mode. Consider using a graphing software to demonstrate how technology can be used to generate the graph. Making a Bar Graph and Finding a Typical Height (Math Journal 1, p. 6) WHOLE-CLASS After all children have been measured, make a bar graph using the class line plot of heights. Review the title of the graph and the labels of the axes. Point out that inches is the unit that goes with all of the numbers on the bottom axis. Have children fill in the numbers of inches from the line plot. Together with children, count the number of stick-on notes for each height. Then have children color that number of squares above each height on the graph. Ask children questions about the data, such as the following: How many children are 42 inches tall? How many children in our class have their heights recorded in this bar graph? How many more children are 48 inches tall than 47 inches tall (or any combination of two heights)? How many fewer children are 42 inches tall than 43 inches tall (or any combination of two heights)? As you ask questions like those listed above, encourage children to ask their own questions that can be answered using the graph. Ask questions such as the following to guide them: What question can you ask that can be answered using this graph? What other questions can you ask that compare the data in one column with the data in another column? After children have asked questions about the graph, discuss how the tallest bar on the graph shows a typical height for the class. Have children record that height in their journals. Then children can use their data to predict the typical height of all first graders in their school or neighborhood. 310 Unit 4 Measurement and Basic Facts
2 Ongoing Learning & Practice Using 8 and Pennies in Two-Fisted Penny Addition (Math Masters, p. 5) PARTNER This activity is a continuation of the systematic record of complements of the numbers 5 to 18 begun in Lesson 4-2. Encourage children to find and record all of the complements of 8 and. 4 2 5 2 3 3 2 1 4 4 1 0 5 5 0 Teaching Master Two-Fisted Penny Addition Summary 6 0 6 1 5 2 4 3 3 4 2 5 1 6 0 7 0 7 1 6 2 5 3 4 4 3 5 2 6 1 7 0 8 0 8 1 7 2 6 3 5 4 4 5 3 6 2 7 1 8 0 Order of numbers may vary. 0 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 0 Math Boxes 4 7 (Math Journal 1, p. 70) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-5. The skills in Problem 4 preview Unit 5 content. Math Masters, p. 5 Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 4 Use Math Boxes, Problem 4 to assess children s ability to solve easy dice sums. Children are making adequate progress if they are able to count the dots to find the sums. [Operations and Computation Goal 1] Student Page Time Math Boxes 1. How long is the line segment? 2. Favorite Drinks, Ms. Brown s Class Fill in the circle next to the best answer. A. about 3 inches B. about 2 inches C. about 1 inch D. about 4 inches 3. Count back by 2s. 36, 34, 32, 30 24 18 28 26 22 20, 16, 14,,,,,, milk juice soda water How many children like milk? 6 children Do more children like juice or soda? juice 4. Write the sums. 7 10 7 Math Journal 1, p. 70 Lesson 4 7 311
HOME LINK 4 7 Family Note Home Link Master Domino Dots Dominoes are a great way to develop readiness for addition and subtraction facts. We will do a lot of work with dominoes this year. Please return this Home Link to school tomorrow. Draw the missing dots on each domino. Write the total number of dots. 1. 10 2. 12 3. 11 Home Link 4 7 (Math Masters, p. 103) INDEPENDENT Home Connection Children draw domino dot patterns and record the total number of dots on dominoes. 8 2 6 6 5 6 4. 5. 6. 3 Differentiation Options 4 5 7 2 3 6 Practice 7. Count up by 5s. 25 65 30 70 10, 15, 20,,, 35,, 45,, 55, 60,,, 75 40 50 8. Count up by 10s. 60, 70, 80, 0, 100, 110, 120, 130 Math Masters, p. 103 ENRICHMENT Estimating Length on a Geoboard (Math Masters, p. 104) PARTNER 5 15 Min To apply children s estimation skills with linear measurement, have them make shapes on the geoboard by estimating their lengths. Have one partner try to make the shapes described on Math Masters, page 104. Then have the other child measure the lengths to see how close the estimates were. Allow children to change roles. Have them explain which lengths were easiest to estimate and why. EXTRA PRACTICE SMALL-GROUP Minute Math+ 5 15 Min Teaching Master Use Minute Math+, pages 18, 53, and 58, to provide practice describing and identifying shapes. Math Masters, p. 104 312 Unit 4 Measurement and Basic Facts