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Ernestine Saville-Brock
Elementary Balanced Math MNPS Numeracy Coaches Ernestine Saville-Brock Math Coordinator Introduction of Presenters collier,pedigo 2010
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A Starting Point for Problem Solving
Many children think of mathematics as a subject that relies on their memorizing facts and practicing skills. But, the true test of children’s success in mathematics is when they can’t remember a fact or have forgotten a skill, they are able to think, reason, and solve problems and make sense of mathematical ideas. Marilyn Burns collier,pedigo 2010
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Norms I commit to… beginning and ending on time
turning my cell phone to vibrate respecting everyone’s opinion processing our learning actively participating and having fun learning together
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Explain Team Mats collier,pedigo 2010
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Round Robin Share Name Where do you teach? What grade do you teach ?
What is one thing most people do not know about you? Number One starts - Share your name, where you teach, what grade, and one thing most people do not know about it. collier,pedigo 2010
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Agenda Mental Math and Math Review Morning Break
Concept Lesson (Day 1 and 2) Lunch - 1 hour 15 minutes Concept Lesson (Day 3 and 4) Afternoon Break Concept Lesson (Day 5) Closure Don’t forget to share where the restrooms are located. collier,pedigo 2010
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Parking Lot Questions throughout the day can be put on post it notes and placed in the parking lot collier,pedigo 2010
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MNPS began implementing several years ago
Balanced Math MNPS began implementing several years ago District initiative all schools and all teachers are to fully implement Balanced Math Balanced Math is district wide collier,pedigo 2010
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Elements of Balanced Math
Conceptual Understanding Problem Solving Computational Fluency Conceptual Understanding is the Why Computational Fluency is defined as being able to compute efficiently and accurately. (Fact Recall) Problem Solving is the application. Concepts and Computation support and strengthen problem solving skills collier,pedigo 2010
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Implementation of math components
Balanced Math is... Standards based Student centered Implementation of math components Research based Best practices Workable schedule Becomes routine You are already doing these Time for all components How do I get it all in? Students do better with routines and consistency collier,pedigo 2010
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Supports Balanced Math Supports Balanced Math
Course Outlines K-2 Common Core Standards Mandatory Pacing Resources Activities Supports Balanced Math 3-4 Tennessee Standards Mandatory Pacing Resources Activities Supports Balanced Math Pacing is mandatory by 9 weeks collier,pedigo 2010
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Does this meet my current standards?
You should be asking this all the time. Planning, Teaching, Reteaching, Assessing, etc….. collier,pedigo 2010
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Elementary Balanced Math Training
Wikispaces Course Outlines Elementary Balanced Math Training K-2 Common Core outlines will be available June 13 3-4 stays the same collier,pedigo 2010
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Balanced Math Framework Assessment/Math Review Quiz
Day 15 minutes 40 minutes 5 minutes 1 Math Review Mental Math Concept Lesson Menu Problem solving, manipulatives, small groups, centers Closure/ math journals 2 Closure 3 Problem solving, small groups , centers 4 5 Math Facts Practice/ Math Review Quiz Problem-based activities, centers, games, small groups 6 7 8 9 10 Assessment/Math Review Quiz Assessment * Elementary – District Wide at least 60 minutes Everyday does not need to include all parts of the concept lesson choices 3rd and 4th Grade – Benchmark Assessments Today we will address grade levels k-4 activities. It may or may not meet your grade level Think of ways to adapt the activities to meet your needs collier,pedigo 2010
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Math Review Typically, this involves the teacher posting 4-6 varying math concepts for students to work. The teacher acts as a facilitator who encourages a variety of ways to solve problems and helps model efficient thinking when necessary. Students solve problems in their math journals or notebooks. Correct together and students take turns sharing their individual strategies with the class. Concepts are consistently revisited throughout the year so that they are not taught in isolation and/or forgotten. Must be current Grade Level Standards Many purchased reviews do not explicitly go over common core and TN standards. Exercise for your brain collier,pedigo 2010
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Daily Math Review 295 + 486 600 - 247 9 x 6 = ___ ___ days = 2 weeks
5 hundreds, 4 tens, 3 ones = _____ 295 + 486 600 - 247 9 x 6 = ___ ___ days = 2 weeks ___ min.=1hr. ___ in. = 1 ft. Kagan Strategy – Think-Write-Rally Robin - Individually Solve and Write Answers. Take turns sharing their thinking process for the addition or subtraction. Starting with Number 2 Number 2 will share out one of the strategies they used or their table 599 Possibilities = 486 – 5 = = 353 Place value Addition Subtraction Multiplication Measurement collier,pedigo 2010
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Did you notice? Debrief – teaching strategies
Several ways to solve a problem. Giving Students time to discuss different strategies collier,pedigo 2010
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Elementary Balanced Math Training
Wikispaces Math Review Elementary Balanced Math Training DEA – Cut and Paste into Template collier,pedigo 2010
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Mental Math “Math on Your Feet” Opportunities to solve problems
Brief daily sessions Opportunities to practice mental computation Opportunities to solve problems in a variety of ways Could occur during transition times “Off Your Seat” – Could Quote brain research Marcia Tate - Children can focus about 1 minute per year of age up to 20 minutes - the longest an adult focus collier,pedigo 2010
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Ten Frames
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Combine these frames! How many do you see??
Ten Frame Dots Combine these frames! How many do you see??
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Have you practiced making combinations of five and ten?
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You are getting faster at this! Keep practicing!
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Numbers About Me Personal Posters – use a fraction and a number with a decimal Mileage on car Height in cm. Marriage Children Pets Years teaching Siblings House number collier,pedigo 2010
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Fit the Facts All About Jamal Numbers 49 2 6 27
Jamal is in grade ______. He is _______ inches tall. His pencil is ________ inches long. Jamal’s dog, Sammy, weighs _______ pounds. Numbers Reasonable Numbers and Number Sense What did you learn collier,pedigo 2010
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Mental Math One more/one less, before/after, a given number
Counting by twos, fives, tens Doubles Fact families Measurement (time, money, calendar, feet, etc.) Math Vocabulary/Math Word Wall Addition &/ or Subtraction Facts Estimation Math Around the Room Count by 2’s starting with 7 Silent Math Hand signals collier,pedigo 2010
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Elementary Balanced Math Training
Wikispaces Mental Math Elementary Balanced Math Training collier,pedigo 2010
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Questions How might you implement mental math and math review? What do you think is the importance of these? Share with you’re Shoulder Partner ( A) goes first collier,pedigo 2010
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“Tell me and I’ll forget. Show me, and I may not remember
“Tell me and I’ll forget. Show me, and I may not remember. Involve me, and I will understand”. -Native American Proverb Break collier,pedigo 2010
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Concept Lessons Students experience inquiry-based methods of understanding key concepts Use of concrete representation when introducing new concepts Problem-based interactive learning should be the foundation in teaching for understanding Teachers implement strategies that help students develop understanding Utilize resources and methods beyond the adopted textbook Opportunities to work with small group instruction, enrichment, etc 1. So that they understand why 2. Manipulatives – Help Construct Making Math Relevant Interactive is key to building understanding 5 Text does not meet some new standards 6. As needed collier,pedigo 2010
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Does this meet my current standards?
You should be asking this all the time. Planning, Teaching, Reteaching, Assessing, etc….. collier,pedigo 2010
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EXAMPLE Balanced Math 1 week Framework
Day 15 min 40 minutes 5 minutes 1 Math Review Mental Math Concept Lesson Menu (Choose one or combination) problem solving manipulatives literature connection small groups/ centers Closure 2 Concept Lesson Menu 3 4 5 Assessment Math Review Quiz Small Group Activities-centers/stations, games, problem solving
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Balanced Math Rotations MNPS Tube
B goes first – shoulder partner Share something from the video that you found useful or that you might like to implement collier,pedigo 2010
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Measurement Vertical Alignment Grades K - 5
Grade K Grade 1 Grade 2 Recognize tools for weight, length and temperature Make direct and indirect comparisons between objects Standard vs. non-standard Estimate and measure using and recognizing appropriate tools Use comparative words Use a thermometer to measure temp. Estimate, measure and calculate length to the nearest inch/cm Use a ruler Read thermometers Weight to nearest lb. or kilo. Grade 3 Grade 4 Grade 5 Nearest half inch & cm Know common equivalencies for length Use fractions with liquid measures Weight to the nearest ounce or gram Calculate perimeter choose reasonable units of measure solve problems Nearest ¼ inch Length Area Perimeter Capacity Weight Number & letter coordinates on grids Perimeter and area of rectangular figures Area of triangles and parallelograms, perimeter and area of irregular shapes Length of line segments in 1st quadrant of coordinate system using fractions & decimals Record measurements in reasonable degree using decimals/fractions This is an example of a vertical alignment, We are currently updating the vertical alignment to match common core standards. collier,pedigo 2010
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Balanced Math Framework
EXAMPLE Balanced Math Framework Measurement Day 15 min 40 minutes 5 minutes 1 Math Review Mental Math Concept Lesson Menu Grandma Activity Literature Link How Big is a Foot? Closure vocabulary cards 2 Manipulative Activity Super Source Kit -Tour of the Islands 3 Problem Solving-Performance Task Stand Up, Hand Up, Pair Up 4 Small groups & centers Differentiated Dinner Menu Intervention groups 5 Assessment Math Review Quiz Formative Assessment Measurement Olympics Talk about day 1 – Grandma will be in Balanced Math in Practice collier,pedigo 2010
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Day 1 Day 15 min 40 minutes 5 minutes 1 Math Review Mental Math
Concept Lesson Menu Grandma Activity Literature Link How Big Is a Foot? Closure math journals vocabulary cards collier,pedigo 2010
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Day 2 2 Math Review Mental Math Concept Lesson Menu
Manipulative Activity Super Source Kit Tour of the Islands Closure/ math journals collier,pedigo 2010
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Tour of the Islands This is a game for 2 to 4 players
The object is to be the first to land on each of the islands on the game board and then return to the Mainland. Each player chooses a different-color crayon or marker to record his or her plays on the game board map. Decide who goes first. The first player puts an X anywhere on the Mainland to mark a starting point and decides which island to visit first. Each player announces an estimate of the distance on the map from the starting point to the island. Then, starting at the X, the player lays down a train of Cuisenaire Rods equal to the estimate so that the train extends in the direction of the first island. The player then marks where the train ends. If the train reaches the island, on the next turn the player can proceed in the same way to any other island. If the train does not reach the island, the player must “tread water” and try to reach the island from this location on the next turn. Each player chooses a different starting point on the Mainland, marks it with an X, and follows the same procedure to go from island to island in any order. Players take turns. When players have visited all the islands, they use the same procedure to return to their starting point on the mainland. The player who returns to the starting point first is the winner. After the activity – Did estimates get better? Short or long distance easier? Extend – Keep up with centimeters for game total Create own game board and directions What other standards? Measure Centimeters, Estimation, Addition collier,pedigo 2010
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Closure Choose two islands on the map and write a set of directions for how to estimate and find the distance between them. Allow time for teachers to do closure collier,pedigo 2010
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Share with you’re Shoulder Partner ( B) goes first
Another Question – How might you adapt this lesson collier,pedigo 2010
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Closure What - Representations of key concepts and relevant connections . Opportunity to use math vocabulary/word wall in context. Students articulate their thinking including pictures and words. Why - Writing can assist math instruction in two ways - by helping children make sense of mathematics and by helping teachers understand what children are learning. When – Typically, this occurs at the conclusion of math class. It should take only a few minutes of the lesson. Where – Math class How - Math Journals Vocabulary Exit Tickets Why – Formative Assessments Math Journals – Closure of Concept Lesson Vocabulary – Create, illustrate , and define vocabulary words Exit Tickets – 1 min – List as many things as you can that come in 2’s, 3’s, etc… Closure Workshop ½ day C collier,pedigo 2010
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Does this meet my current standards?
You should be asking this all the time. Planning, Teaching, Reteaching, Assessing, etc….. collier,pedigo 2010
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C R A Model Representational
1st Students will use their prior knowledge to construct concrete representations of math. 2nd Students must represent their understanding in a reflective &/or symbolic form. 3rd One or both forms will be a visual reminder for the understanding of the higher-thinking abstract. Representational Closure supports this representational stage Abstract Concrete collier,pedigo 2010
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Where to find Concept Lessons
Instructional Coaches Super Source Manipulative Kit Marilyn Burns Math Lessons Marilyn Burns Math and Literature Online resources Math Games Textbook Teacher Resource books Navigations Series (NCTM) AIMS Show examples of these materials 54
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Music imprints an instructional message in the human brain 90%
faster than any other learning strategy. Music with the Brain in Mind Eric Jensen Lunch Break collier,pedigo 2010
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How many rectangles can you find in the grid below?
Is the answer really important? It’s the process. collier,pedigo 2010
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I Have Who Has
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Balanced Math Framework Measurement
EXAMPLE Balanced Math Framework Measurement Day 15 min 40 minutes 5 minutes 1 Math Review Mental Math Concept Lesson Menu Grandma Activity Literature Link How Big Is a Foot? Closure vocabulary cards 2 Manipulative Activity Super Source Kit - Tour of the Islands 3 Problem Solving-Performance Task Stand Up, Hand Up, Pair Up 4 Small groups & centers Differentiated Dinner Menu Intervention groups 5 Assessment Math Review Quiz Formative Assessment Measurement Olympics collier,pedigo 2010
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Day 3 3 Math Review Mental Math Concept Lesson Menu Problem Solving
Performance Task Stand Up, Hand Up, Pair Up Closure math journals Mention and explain briefly Save for end of day, if needed collier,pedigo 2010
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A problem is defined by…
Any task or activity for which a student has no prescribed or memorized rules or methods, nor is there a perception by the student that there is a specific “correct” solution method. Application of facts and concepts Critical thinking If the problem is too easy, its not a problem, but an excercise Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics Educational Researcher, 25 (May), 12-21 collier,pedigo 2010
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What are some ways to incorporate more problem solving?
Mini-lessons Tasks that do not require the entire class period—the think-pair-share strategy is useful. Workstations and games Can be setup around the room without the need to distribute and collect materials to allow students to work on different tasks and concepts. Problem-solving Menu A menu is a collection of activities for a student to do. A menu can provide differentiated class work activities for several days, a week, or a longer period of time. The tasks on the menu are not hierarchical and do not conceptually build upon each other. collier,pedigo 2010
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Check your work Model Numbers Words Answer
(Draw a picture or diagram, or make a list, table, chart, or graph). Numbers (Show how worked each part of the problem). Words To solve this problem, first I had to _____________________________. Then, I________________________. Next, I _______________________. After that, I ___________________. Finally, I found out that __________ ______________________________. Answer collier,pedigo 2010
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Problem Solving Resources Elementary Balanced Math Training
Wikispaces Problem Solving Resources Elementary Balanced Math Training Problem Solving Workshop ½ day training collier,pedigo 2010
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Day 4 Differentiated Dinner Menu Intervention Groups 4 Math Review
Mental Math Small groups & centers Differentiated Dinner Menu Intervention Groups Closure/ math journals Small group is reason/focus Through observation and formative assessment, need to pull small group for remediation, enrichment, etc…. collier,pedigo 2010
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Side Dishes (Select __)
Dinner Menu Main Dish (Select __) Measure the length of the objects in the measurement container using any of the nonstandard units we have used in class. Using your vocabulary cards, play “Show me the word that means…” with a partner Complete Measurement Scavenger Hunt activity. Use machine tape and follow directions to create Season’s By the Yard. Side Dishes (Select __) Use a ruler to draw and label lines for the following measurements: 10 inches, 5 inches, 3 centimeters, 15 centimeters, 1 foot, 1 inch, 3 inches, and 10 centimeters. Organize the pictures of the objects in order from smallest to largest. In partners, use your vocabulary cards. Partner A turns to word side and partner B turns to definition. They match cards. Complete Perfect People activity with a partner. Dessert (Select __) Draw a map of Tennessee. Label 4 locations on your map with a large dot. Using you ruler draw lines to connect these locations. Measure and label these lines on your map to the nearest inch. Write a story problem on an index card that can be solved using your map. Using your vocabulary cards, choose 3 cards and list at least 3 examples of each word. Create measurement layer book foldable. Measure and record items from tub. Some Students in a small group and others work on tasks Students do not need the same amounts of tasks on menu because they might have different amounts of time. Teacher selects how many in each category for different students. We choose 3 for you collier,pedigo 2010
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Afternoon Break
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Day 5 5 Assessment Math Review Quiz Formative Assessment
Measurement Olympics collier,pedigo 2010
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Measurement Olympics Ask for volunteers for each event
Have participants record estimates before each event collier,pedigo 2010
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Assessments FORMATIVE—checking on learning as students progress SUMMATIVE—checking on learning at the end of the learning experience collier,pedigo 2010
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Assessment “When the cook tastes the soup, that’s formative; when the guests taste the soup, that’s summative.” (Stake, 2005) collier,pedigo 2010
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Formative & Summative Assessments
Teacher Observation Math Journals Teacher Made Tests Chapter and Unit Tests Easy CBM Math (DIBELS) Discovery Education Assessments Benchmark Assessments Projects TCAP collier,pedigo 2010
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Elementary Balanced Math Training
Wikispaces Math Sites Elementary Balanced Math Training
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Balanced Math is standards based, not textbook based
collier,pedigo 2010
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Exit Ticket What is the most significant thing you learned about Balanced Math? What component will you implement first and with what math standard? What support do you need next as you implement Balanced Math?
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Elementary Balanced Math
Presented by MNPS Elementary Numeracy Coaches Ernestine Saville-Brock MNPS Mathematics Coordinator K-12
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Bibliography Five Easy Steps to a Balanced Math Program for Primary Grades by Larry Ainsworth and Jan Christinson
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