I NTRODUCTIONS Welcome! Please be sure to sign in and get a notebook. Then create a name plate with the following information: Name School Years teaching math On one of the charts, indicate your comfort level for teaching the Common Core beginning in August. Place a post-it note on the appropriate chart.
S CHEDULE 8:30-9:00 Puzzling Norms Activity (Revisit daily.) 9:00-9:30 CCSS Overview & Cookie Dough Task 9:30-10:30 Standards for Mathematical Practice 10:30-10:45 Break 10:45-12:00 Unpacking the Common Core 12:00-1:15 Lunch 1:15-2:45 Investigations Connections (feel free to take a break as needed) 2:45-3:30 Materials and Activities
C OMMON C ORE S TATE S TANDARDS …A Q UICK R EVIEW /P REVIEW K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability Traditional US Mathematics Approach
Operations and Algebraic Thinking Expressions and Equations Algebra Number and OperationsBase Ten The Number System Number and Operations Fractions K 12345678High School C OMMON C ORE A PPROACH
H OW IS THE C OMMON C ORE A LIGNED V ERTICALLY ? R ETRIEVED FROM ACHIEVETHECORE. ORG Grade: Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction-- concepts, skills, and problem solving 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional relationships; early expressions and equations 7 Ratios and proportional relationships; arithmetic of rational numbers 8 Linear algebra GradeStandard Required Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within 10 22.OA.2 2.NBT.5 Add/subtract within 20 Add/subtract within 100 33.OA.7 3.NBT.2 Multiply/divide within 100 Add/subtract within 1000 44.NBT.4Add/subtract within 1,000,000 55.NBT.5Multi-digit multiplication 66.NS.2,3Multi-digit division Multi-digit decimal operations
C OMMON C ORE S HIFTS FOR M ATH FOCUS- Strongly where the standards focus COHERENCE- Think across grades and link to major topics within grades (trajectory) RIGOR- In major topics; pursue conceptual understanding, procedural skill and fluency, and application www.achievethecore.org
T HINK ABOUT A PRESENT …. If you took something old from your house and wrapped it in a new box with a shiny bow, does it make it a new gift? Likewise, taking the old NCSCOS and squeezing it into the new Common Core will not change the face of education. How do you think the Common Core will change math instruction?
C ONTENT E MPHASIS B Y C LUSTER Take a look at the Content Emphasis in 3 rd Grade. What do you notice? What major clusters are in 3 rd grade? What clusters support the major ones? How do major and supporting clusters differ?
Q UICK Q UIZ Using the information that you have so far about the 3 rd grade Common Core State Standards, where do you think 3 rd grade will primarily focus? DOMAIN Operations and Algebraic Thinking Number and Operations Base Ten Number and Operations Fractions Measurement and Data Geometry Total Percentage of the Entire Core 30-35% 5-10% 20-25% 22-27% 10-15% 100% Old Percentages 20-25% 35-40% 10-12% and 12-15% 12-15% 100%
C OOKIE D OUGH T ASK Chocolate Chip Cookie Dough $5 a tub Peanut Butter Cookie Dough $4 a tub Oatmeal Cookie Dough $3 a tub 1.Jill Sold 2 tubs of Oatmeal Cookie Dough. How much did she raise? 2.Joe sold 4 tubs of Peanut butter Cookie Dough and 4 tubs of Chocolate Chip Cookie Dough. How much money did he raise in all? Show how you figured it out. 3.Jade sold only Peanut Butter Cookie Dough. She raised $32. How many tubs did she sell? Show how you figured it out. 4.Jermaines mother loves oatmeal cookies. She has $20 to spend. What is the greatest number of tubs of oatmeal cookie dough she can buy? Explain how you figured this out.
C OOKIE D OUGH T ASK : L OOKING AT S TUDENT W ORK Utilize the rubric to score yourself. Then, exchange your work with someone at your table. Score each others work using the rubric. What information did you gain about students understanding via the task and rubric? What would your next steps be instructionally after utilizing this task?
S TANDARDS FOR M ATHEMATICAL P RACTICE Think about the Cookie Dough task. What mathematical practices were embedded in the task? Todays Focus… Standard 4- Model with Mathematics Standard 7- Look for and Make use of Structure Standard 8- Look for and Express Regularity in Repeated Reasoning
S TANDARDS FOR M ATHEMATICAL P RACTICE ! Peruse the MP4, MP7, & MP8 located at the beginning of your Common Core State Standards. On a sticky note and in your own words… Write a word, phrase, or sentence and/or draw a picture/caption that best describes each practice. Post your sticky notes onto the relative charts around the room.
M ODEL WITH M ATHEMATICS Calls for students to interact with their everyday world through play and to explore the mathematics. Think about size, shape and fit, quantity, and number. Students should begin to understand that mathematics is not just a collection of skills whose only use is to demonstrate that one has them. Ensure that the mathematics that students are engaged in helps them see and interpret the world.
A L OOK AT THE REAL WORLD Sam Houston Elementary School has nearly 1,000 children from kindergarten through 5 th grade, with about the same number of students in each grade. No class has more than 25 students, but most classes are close to that. What can you figure out from this information? How does this problem allow students to Model with Mathematics?
L OOK FOR AND M AKE USE OF S TRUCTURE Think about how students are typically taught to add fractions with a like denominator. How is that different from the following: If 2 sheep plus 3 sheep is 5 sheep and two hundred plus three hundred equal 5 hundred, then would 2/8 + 3/8 = 5/8
L OOK FOR AND M AKE U SE OF S TRUCTURE Without solving the following which symbol would you put in the blank: (>, <, =) X +5 ________ X + 4 How did you know? This standard involves students thinking about the way things work (mathematical thinking) and applying that to other problems.
L OOK FOR AND E XPRESS R EGULARITY IN R EPEATED R EASONING Choose three numbers in a row (5, 6, 7 for example). Compare the middle number times itself to the product of the two outer numbers. Do this several times, then without solving tell what the answer is to 29 x 31. Explain the pattern in the problem to a partner.
A C LOSER L OOK AT THE P RACTICES Looking back at the cookie dough task, what practices were evident? Watch the following video. Record when and how the teacher uses practices 4, 7, and 8. Standards for Mathematical Practice Video
U NPACKING THE S TANDARDS Critical AreaCCSSWhat does it say in your own words? By the end, what can students do? Give an example of a task in a lesson or assessment. Developing Understanding of multiplication and division strategies for multiplication and division within 100 3.OA.3- Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities 3.OA.4- Determine the unknown whole number in a multiplication or division equation relating three whole numbers. 3.OA.5- Apply properties of operations as strategies to multiply and divide 3.OA.7- fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division
T ASK #1 - C ONSTRUCTING A N A RRAY Build a 6 x 3 array using colored tiles (in one color). What is the product (number of tiles)? Use the 6 x 3 array to build a 6 x 9 array (possibly another color). How did a 6 x 3 array help you figure out the product of 6 x 9?
T ASK #3 – C OUNTING A ROUND THE C LASS Count around the class by 4s. What would be a multiplication equation that would represent 6 people counting by 4s? Predict what the 10 th person say? the 20 th ? Turn and tell… Explain your reasoning to a partner. What is the value of this activity? (p. 155, lesson 1.3)
W HAT DOES FLUENCY REALLY MEAN ? Efficiency implies that the student does not get bogged down in too many steps or lose track of the logic of the strategy. An efficient strategy is one that the student can carry out easily, keeping track of subproblems and making use of intermediate results to solve the problem. Accuracy depends on several aspects of the problem- solving process, among them careful recording, knowledge of number facts and other important number relationships, and double-checking results. Flexibility requires the knowledge of more than one approach to solving a particular kind of problem, such as two-digit multiplication. Students need to be flexible in order to choose an appropriate strategy for the problem at hand, and also to use one method to solve a problem and another method to double-check the results. Retrieved from http://investigations.terc.edu/library/bookpapers/comp_fluency.cfm
H OW IS FLUENCY WITH MULTIPLES FOSTERED IN YOUR CLASSROOM ?
T ASK #4 – N UMBER L INES FOR M ULTIPLICATION Use a sentence strip or piece of adding machine tape to create a number line from 0 to 30. Above the line, represent skip counting by 5. Below the line, represent skip counting by 6. What do you notice?
A UTHENTIC A SSESSMENT P ROBLEM - P ERFORMANCE T ASK You want to rearrange the furniture in some room in your house, but your parents do not think it would be a good idea. To help persuade your parents to rearrange the furniture you are going to make a two dimensional scale model of what the room would ultimately look like. http://jfmueller.faculty.noctrl.edu/toolbox/examples/seaver/re arrangeroomtask.htm http://jfmueller.faculty.noctrl.edu/toolbox/examples/seaver/re arrangeroomtask.htm
M ULTIPLICATION AND D IVISION - CGI Use the chart provided to sort the problems by problem types that students encounter. When you are done, check your work via Table 2 (p. 89 or 32) in the Common Core. Next, remove the cards and write new problems with your group that correlate with the problem types.
W HAT I S C OGNITIVELY G UIDED I NSTRUCTION (CGI)? Students spend most of their time solving problems related to a book read to them, a unit they have studied, or something going on in their lives Various materials are available to them at all times to assist in problem solving, and each student selects the materials they want to use. Students are not shown how to solve the problems, instead each child solves them in any way that they can, sometimes in more than one way, and reports how the problem was solved to peers and teachers The teacher and peers listen and question the student until they understand the problem solutions, and then the entire process is repeated Using information from students reporting, teachers make decisions about what each child knows and how instruction should be structured to meet each childs needs.
CGI What are some of the Benefits of exposing students to different problem types (CGI)? Which problem type are students least exposed to? Which type supports the Common Cores rigor requirement?
L UNCH T IME ! Take a brain break…. Enjoy your lunch! We will reconvene at 1:15 pm.
I NVESTIGATIONS C ONNECTIONS Math Workshop: Product Game Factor Pairs Arranging Chairs CGI Problems Math Playground Use the template to record your thoughts as you work your way through the various games and activities within Investigations.
S ELECTED R ESPONSE (SR) S AMPLE T EST I TEM SBAC Marcus has 36 marbles. He is putting an equal number of marbles into 4 bags. For 1a–1d, choose Yes or No to indicate whether each number sentence could be used to find the number of marbles Marcus puts in each bag. 1a. 36 x 4 Yes No 1b. 36 ÷ 4 Yes No 1c. 4 x = 36 Yes No 1d. 4 ÷ = 36 Yes No
C ONSTRUCTED R ESPONSE (CR) S AMPLE T EST I TEM SBAC A roller skating team has 10 members. Each team member has 2 skates. Each skate has 4 wheels. What is the total number of skate wheels that the team has? wheels
E XTENDED R ESPONSE (ER) S AMPLE T EST I TEM SBAC Brandon learned that, beginning at age 2, children grow about 6 centimeters per year. Brandons brother is 2 years old today and 80 centimeters tall. Brandon wants to estimate what his brothers height would be at age 7. Use pictures, math, or words to explain the work needed to find his brothers height. Brothers height at age 7 will be about centimeters.
P ERFORMANCE T ASKS (PT) S AMPLE T EST I TEM SBAC Ideal Tasks – Reflect a real-world task and/or scenario-based problem – Require students to engage in 1 or more Standards for Mathematical Practice – Allow for multiple approaches – Take time (one or more class periods) to solve.
ACRE : A CCOUNTABILITY AND C URRICULUM R EFORM E FFORT L EARN MORE ABOUT THE FUTURE OF N ORTH C AROLINA P UBLIC S CHOOLS ASSESSMENT P ROGRAM BY VISITING THE N.C. P UBLIC S CHOOLS W EBSITE (DPI) 3rd-ccssm-pd-062012-dp 2nd revision.pptx
T HE D OORBELL R ANG T HE D OORBELL R ANG BY P AT H UTCHINS Task: Grandma came at the end of the story and brought a tray of more cookies to share. If Grandma brought 5 dozen cookies over when she came, and the number of children was doubled, how many cookies would each child get? Explain how you got your answer. Extension: Switch solutions with another group and determine whether their solution or your solution is a more efficient way to solve the problem. What is your reasoning?
E ACH O RANGE H AD 8 S LICES Foldable Activity! Fold paper hot dog style and place it like a tent in front of you. Cut the front part of the tent into fourths. Create 4 of your own story problems similar to those in the story. Write the problems on the front flaps. Flip up the foldable page and write the equation (including a symbol for the unknown). Also, write other related problems using the unknown. Switch your foldable with a partner and solve the problems on the back of the foldable. Use a different strategy for each problem. Return foldable. Look at how they solved your problems and determine if their work is correct. Let your partner know what you think and why.
H OMEWORK Read Teaching in Grades 3 and 4: How is each common core state standard for mathematics different from each old objective? Why must we look at the unpacking documents? Why should we look at the crosswalk documents? What are the differences between the old standards and the new Common Core? What are the implications for task work? Why focus on the Standards for Mathematical Practice?
I T S P RESENT T IME … You will receive…. The Doorbell Rang Each Orange Has 8 Slices
EXIT CARDS! What is something you learned today that is new and/or different? How do you plan to use it?
Mayor Mason has raised money for a new park that is 800 yd by 800 yd. He divides the park into various sections: He starts by dividing the park into 4 square sections. The NE section is divided into 8 equally-sized triangular sections The NW section has 2 triangular sections and 2 rectangular sections, and all 4 sections are the same size The southeast section has 16 equally sized square sections The southwest section has 2 equally-sized triangular sections that together make up 1 / 3 of the section, 4 equally-sized rectangular sections that together make up 1 / 6 of the section, and equally-sized rectangles that make up the rest of the southwest section. For each section, find its area as a fraction of the entire region.
A C LOSER LOOK AT THE READING …. What is the importance of looking at the old standards? Looking at the unpacking,what has changed in 3 rd grade with regards to fraction development? How does the CCSS differ from the NCSCOS with regards to teaching and expectations? According to p. 501, what are the implications for task work within the common core? According to the article, what are the implications for the Standards for Mathematical Practice?
S TANDARDS FOR M ATHEMATICAL P RACTICE Standard 2- Reason Abstractly and Quantitatively Standard 5- Use Appropriate Tools Strategically Standard 6- Attend to Precision Peruse above SMP in your CCSS. Summarize each on a sticky note using a picture/caption, phrase, or sentence. Post onto charts. GALLERY CRAWL!
R EASON A BSTRACTLY AND Q UANTITATIVELY Write as many numerical expressions as you can that describe the tiles in this figure. Did you have- 1+2+3+4+3+2+1 or 1+3+5+7 or 10 +6 What about this? 8 + 8
How many busses are needed for 99 children if each bus seats 44? If the child can solve and get 2 r 11, 2 ¼ or 2.25, they have AN answer. But if they can take that answer and reason/interpret that 3 buses are needed, then they are reaching this standard (MP2).
MRI Math Reasoning Inventory Site Math Reasoning Inventory
H OW DID YOUR PARTNER RESPOND ? Converted to common denominators Compared to 1/2 or 50%, or 1 or 100% (e.g., 5/6 is more than 1/2 and 3/8 is less than 1/2) Explained that eighths are smaller than sixths and there are fewer eighths Converted to decimals or percents Gave other reasonable explanation Guessed, did not explain, or gave faulty explanation
U SE A PPROPRIATE T OOLS S TRATEGICALLY Requires the classroom to be comprised of choice tools readily available for problem solving Calls for students to develop the ability to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations Think about the following tools: Number line, hundreds board, color tiles When would it be helpful to use these and when might it be limiting?
A TTEND TO P RECISION The focus of this standard is not only about accurate calculations (correct answer), but about precision of communication in: Speech Written symbols, and In specifying the nature and units of quantities
Chocolate Chip Cookie Dough $5 a tub Peanut Butter Cookie Dough $4 a tub Oatmeal Cookie Dough $3 a tub 1. Jill sold 2 tubs of Oatmeal Cookie Dough. How much did she raise? $ ____________________________ 2. Joe sold 4 tubs of Peanut Butter Cookie Dough and 4 tubs of Chocolate Chip Cookie Dough. How much money did he raise in all? $ _________________________________ Show how you figured it out. 4 3. Jade sold only Peanut Butter Cookie Dough. She raised $32. How many tubs did she sell? __________________ tubs Show how you figured it out. 4. Jermaines mother loves oatmeal cookies. She has $20. to spend. What is the greatest number of tubs of Oatmeal Cookie Dough she can buy? __________________________ tubs Explain how you figured it out. ______________________________________________________________________________________ Standards for Mathematical Video- 2 W HAT DO THESE P RACTICES LOOK LIKE ? In the task, how and when did you use these practices? What kinds of questions could you ask to make students aware of these practices? What standards were evident in the video?
Critical AreaCCSSWhat does it say in your own words? By the end, what can students do? Give an example of a task in a lesson or assessment. Developing understanding of fractions, especially unit fractions (fractions with numerator 1) 3.NF.1- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b 3.NF.2- Understand a fraction as a number on the number line; represent fractions on a number line diagram 3.NF.3- Explain equivalences in special cases, and compare fractions by reasoning about their size
F ACT OR F ICTION ? Fraction concepts are difficult. Our students (and many adults) struggle with fraction concepts. What we have been doing isnt working. The Common Core is grounded in research about how students come to understand fraction concepts.
B IG I DEA …. The first goal in the development of fractions should be to help children construct the idea of fractional parts of the whole- the parts that result when the whole or unit has been partitioned into equal sized portions or fair shares. – John Van de Walle
L ET S P ARTITION ! With your partner, fold one plate so that each of you get the same amount. Did you get equal amounts? How do you know? Prove it!
F OLD AND FOLD AGAIN ! You and your partner would like two pieces each. So, fold another plate so each of you get two equal pieces. How did you fold the plate? Did you each get equal shares? How do you know? Prove it! What do we call these equi-sized portions? How is the process of folding halves similar/different from folding fourths?
H OW DO WE MAKE FOURTHS ? Half of a half concept
S TUDENTS NEED TO P ARTITION UNMARKED REGIONS ( NO LINES ALREADY DRAWN ). W HY ?
P RE - PARTITIONED REGIONS LEAD TO A COMMON MISCONCEPTION : ¼ 1/3 1/3
D IVIDING THE R OOM You want to share the space in your school closet between you and three other teachers. On grid paper, draw three 6x4 rectangles and label them a. b. and c. Divide each closet according to the directions below: a) 2 sections are rectangles and 2 sections are different shaped rectangles b) 2 sections are rectangles and 2 sections are triangles c) You have 4 different shaped regions
A RE YOU HUNGRY YET ? Take a brain break….be back here at 1:15! Enjoy your lunch!
S CHOOL C ARNIVAL Marilyn is serving strawberry ice cream. Each scoop contains 1/4 of a cup. By the end of her first shift, she has scooped out 4 servings. How much ice cream has she served? Solve the School Carnival tasks on your table. Represent your solutions on a number line and model each with an equation. Glow sticks are a popular carnival prize. A box of glow sticks weighs ¼ of a pound. If I am carrying 7 pounds, how may boxes am I carrying? The water balloon booth has ¾ of a gallon of water left. They need to fill 5 balloons. How much water should they use for each balloon?
P ARTITIONING K-2: Regions 3: Regions and Number lines 4: Strengthen Number lines, regions beginning to fade 5: Number lines
P ARTITIONING A N UMBER L INE Make a number line from 0 to 2. Put the following fractions on the number line 1 / 6, 2 / 6, 5 / 6, 6 / 6, 8 / 6, 11 / 6 Describe your process to the person sitting across from you. Prove that the fractions are in the correct location.
P ARTITIONING A N UMBER L INE Using your number line, solve: You need 1 5 / 6 yards of ribbon for a school project. You find 5 / 6 in your closet, and ask your mom to buy 5 / 6 more. Do you have enough? If not, how much more do you need? If so, how much ribbon will you have left over? Be able to explain using your number line.
P ARTITIONING A N UMBER L INE Create another number line 0 to 2 Plot the following numbers: 1 / 3, 3 / 4, 4 / 3, 2 / 3, 3 / 2 In between each of your fractions, plot another fraction (you should have 9 fractions) Describe your process to the person sitting across from you. Prove that the fractions are in the correct location.
W HY N UMBER L INES ? Easier to divide the whole into equal parts because only length is involved. Addition and subtraction are much more easily modeled. Multiplication and Division are more easily modeled.
U NIT F RACTIONS Unit fractions are the basic building blocks of fractions, in the same sense that the number 1 is the basic building block of whole numbers. Every fraction is a piecing together of unit fractions ( 2 / 5 is 2 copies of the unit fraction 1 / 5).
3NF 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/ b and that the endpoint of the part based at 0 locates the number 1/ b on the number line. Represent a fraction a / b on a number line diagram by marking off a lengths 1/ b from 0. Recognize that the resulting interval has size a / b and that its endpoint locates the number a / b on the number line.
S YMBOLIC R EPRESENTATION OF F RACTIONS Students must be able to think about fractions in a different way than when they are working with whole numbers. The number 34 is viewed as representing a specific quantity. When the same digits (3 and 4) are used in the number ¾, the digits are representing a part/whole relationship.
W HY ARE FRACTIONS DIFFICULT ? Read page 109-110 in Unit 7. What are the big ideas in fraction development? How does the investigations work from this unit aid in developing students understanding?
I NVESTIGATIONS C ONNECTIONS Tangrams Triffle Task (from DPIs Week-by-Week Essentials…) Fractions on a Number Line Fraction Cookie Game Making Fraction Sets- Take 1 of each color sheet Fold the pieces to represent halves, thirds, fourths, sixths, and eighths Cut out 1 piece from each and compare the unit fractions, what do you notice?
A SSESSMENT If 8 people share 4 brownies equally, how much will each person get? Show how you figured this out. What fraction concepts are assessed in this task? What MP are evident?
MRI Recap morning partner activity. Show Amys MRI video. (need link to website) Ask, How will Investigations, the Common Core, and tasks like we did today help build students fraction sense?
I T S P RESENT T IME … Vanna, show them what they will receive…. Beyond Pizzas and Pies
B EYOND P IZZAS AND P IES What do you notice is important about fraction development for the third grade? (section importance regarding unit fractions) Read pages 61-67 independently. Activity 1Pattern Block Fractions What are some ways to incorporate these tasks within your classroom?
H OMEWORK Read Chapter 7 of Beyond Pizzas and Pies Think about real life examples that can be used in your classroom
EXIT CARDS! What is something you learned today that is new and/or different? How do you plan to use it?
P EN FOR P UGSY Lilys mom agreed to adopt a new puppy for the family. Before Lily can bring Pugsy home, she needs to build an exercise pen for him in the backyard. Lily has 36 ft. of fencing. Find all of the rectangular pens that Lily can make. Use the Lilys Backyard sheet in your binder to solve this problem. Questions: How many different pens can Lily make? What is true about the perimeters of all of the pens? How do you know? What do you notice about the area measurements?
A C LOSER LOOK AT THE R EADING H OMEWORK …. Group Project! Create a poster that best summarizes your assigned reading section. Some ideas… Create a comic strip cartoon. Compose and sing a song. Role Play! Poetry Slam!
S TANDARDS FOR M ATHEMATICAL P RACTICE Standard 1- Make Sense of problems and persevere in solving them Standard 3- Construct Viable Arguments and Critique the Reasoning of Others
S TANDARDS FOR M ATHEMATICAL P RACTICE Peruse the MP1 & MP3 located at the beginning of your Common Core State Standards. On a sticky note and in your own words… Write a word, phrase, or sentence and/or draw a picture/caption that best describes each practice. Post your sticky notes onto the relative charts around the room.
M AKE S ENSE OF P ROBLEMS AND P ERSEVERE IN S OLVING T HEM Problem Solvers must: Figure out the right question to be asking What relevant experience we have What additional information we might need And know where to start In addition we must have the stamina to continue even when progress is hard, but enough flexibility to try alternative approaches when progress seems too hard
M AKE S ENSE OF P ROBLEMS AND P ERSEVERE IN S OLVING T HEM How does this questioning approach aid in developing this skill for our students: Eva had 36 green pepper seedlings and 24 tomato seedlings. She planted 48 of them. What questions could be figured our from that information?
C ONSTRUCT V IABLE A RGUMENTS AND C RITIQUE THE R EASONING OF O THERS In writing we say, show dont tell. However, this standard require our students to Show and Tell. Appropriate representations will help students to defend or justify their answers. Example: How many different 5 tall towers of 1 cubes can be made, using exactly one white cube and four blue cubes? How could students construct an argument via this question?
W HAT DOES THIS LOOK LIKE ? While perusing the video, think about what occurred in the task that allowed students to use the standards for mathematical practice? Standards for Mathematical Practice Video 3
A REA OR P ERIMETER ? A GREE /D ISAGREE ? 1. Jess is building a frame to fit a picture he painted. The picture measures 18 inches by 15 inches. About how much wood will Jess need to make the frame? 2. Sam is building a wire fence around his vegetable garden. The garden measures 3 yards by 6 yards. How much fencing will he need? 3. Nora is buying carpet for her living room. The living room measures 12 feet by 15 feet. How much carpet does Nora need to purchase? 4. Tanya is buying a dry erase board for her bedroom wall. The board measures 75 centimeters by 100 centimeters. How much of her wall will be covered by the board? 5. Jordan is buying a new couch for her living room. The couch measures 3 feet wide by 9 feet long. How much of her living room floor will be taken by the couch? 6. Chris is buying wallpaper border for his bathroom. The bathroom measures 2 meters by 3 meters. How much wallpaper border does Chris need to buy?
Critical AreaCCSSWhat does it say in your own words? By the end, what can students do? Give an example of a task in a lesson or assessment. Developing understanding of structure of rectangular arrays and of area 3.MD.5-Recognize area as an attribute of plane figures and understand concepts of area and measurement 3.MD.6- Measure areas by counting unit squares 3.MD.7- Relate area to the operations of multiplication and addition
D EVELOPING A REA AND P ERIMETER - C OMMON C ORE U NIT Directions- Go to 2-3 activities listed below. Identify the standard and mathematical practices for each. Think about how each can be extended. What are the connections between area and perimeter- what generalizations do want students to make? Area and Perimeter Activities- DPI Unit Breaking Apart Arrays 2 Finding Areas of complex figures Perimeter Parade Routes Robotic Racing Pedaling for pennies
L UNCH T IME ! Take a brain break….be back here at 1:15! Enjoy your lunch!
Critical AreaCCSSWhat does it say in your own words? By the end, what can students do? Give an example of a task in a lesson or assessment. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects 3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes 3.MD.2- Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters. 3.MD.4- Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.
L INE P LOT, ELAPSED TIME, PROBLEM SOLVING Make Inch Rulers. Label inches. (Use colored paper.) Measurement Line Plot- See binder. Solve word problems. Elapsed Time on the Number Line EOG Review Lessons on Elapsed Time
I T S P RESENT T IME … Vanna, show them what they will receive…. Dual Dial Platform Scale Volume Liter Containers (ha! Ha! These will arrive to you at your school) Elementary Balance
D UAL -D IAL P LATFORM S CALE AND L ITER V OLUME S ETS Read 3.MD.2 and unpacking for that standard independently. What do you think is the most important to take away from that standard? Solve problems from K-5 Math Teaching Resources Go to site to view resource: http://www.k-5mathteachingresources.com Create word problems for this standard to be posted on wiki/emailed to use in the upcoming year!
E LEMENTARY S CHOOL B ALANCE Draw the following table in your journal: Use your balances to find 3 or 4 objects to measure and fill in the chart. Discuss what you notice about the connection between the units of measure. Support your findings. Communicate your findings and explain the connections. Gallery walk!!! (Do you agree /disagree with other groups?) ObjectKgGMg
EXIT CARDS! How has your math content knowledge been broadened as a result of the STEM Institute? How is teaching and assessing the CCSSM different from teaching and assessing the NCSCOS? How will Investigations help you meet the expectations of the CCSSM?