Sit at tables with other 4 th or 5 th grade teachers, not necessarily from your own school. Did you bring samples of student work on the assessment?. When You Come In…. Multiplication and division follow a learning progression across the grades. 3-4-5 Continuum. Starting Point.
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Sit at tables with other 4th or 5th grade teachers, not necessarily from your own school.
Did you bring samples of student work on the assessment?When You Come In…
Multiplication and division follow a learning progression across the grades.3-4-5 Continuum
Purpose – Develop professional knowledge and effective teaching strategies
Textbooks like Everyday Math and EnVision are important instructional resources, but:
Critical Area 1: Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends;
Critical Area 2: Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers;
Critical Area 3: Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.Common Core for 4th grade
Critical Area 1: Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations;
Critical Area 2: Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions);
Critical Area 3: developing understanding of volume.
Using the Common Core Standards for 3rd-5th grade, make a map of the learning progression for multiplication and division.
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.
• Teachers provide clear models for solving a problem type using an array of examples.
• Students receive extensive practice in use of newly learned strategies and skills.
• Students are provided with opportunities to think aloud (i.e., talk through the decisions they make and the steps they take).
• Students are provided with extensive feedback.
National Mathematics Advisory Panel, 2008Explicit Instruction
• Ensure that instructional materials are systematic and explicit. In particular, they should include numerous clear models of easy and difficult problems, with accompanying teacher think-alouds.
• Provide students with opportunities to solve problems in a group and communicate problem-solving strategies.
• Ensure that instructional materials include cumulative review in each session.Explicit Instruction
The NMAP notes that this does not mean that all mathematics instruction should be explicit.
So what’s the difference?
You need to paint the walls of the cafetorium in your school. You have to figure out how much paint is needed. The walls of the room are 24 feet high. You measure each wall along the bottom, and get these measurements: Wall 1: 53 feet long. Wall 2: 34 feet long, Wall 3: 53 feet long, Wall 4: 34 feet long. There are also two doors in the gym, each is 10 feet high by 8 feet wide, and you don’t have to paint them. How many square feet of paint would you need for one coat on all the walls?When?
Teach students about the structure of various problem types, how to categorize problems based on structure, and how to determine appropriate solutions for each problem type.
Knowledge of the content is interwoven with knowledge of effective teaching strategies to produce deep learning.Braided Knowledge
Concepts of multiplication and division need to be understood through problem situations.
When students are given these kinds of problems and asked to work them in any way they can (and given manipulatives), they generally use these kinds of strategies:
How would you connect the learning progressions (content) with the instructional strategies (practices)? Look back through the powerpoint slides at the content, look at the instructional strategies on the walls.
Looking at the results of the little assessment, can you spot areas that need attention? Whole class or small group?Formative feedback
Megan has 15 cookies. She put the cookies into 5 bags with the same number of cookies in each bag. How many cookies are in each bag?
Megan has 15 cookies. She puts 3 cookies in each bag. How many bags can she fill?Basic division concepts
Choose something from today’s session (or a couple things) to try before the next session. Come back with examples of students’ work from what you tried.