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Lucy West

Welcome & Enjoy Breakfast Please sit by grade levels—k, 1, 2, 3, 4, 5, 6+ While you are having breakfast and networking will you please: Make an estimate for all of the jars and boxes. Use post-its Write large using MARKER Place your post-it on the appropriate chart paper Enjoy your breakfast and networking with colleagues

Agenda Exploration of Estimation Estimation, Reasoning and CCSS Practices Multiplication Patterns and Conjectures ELL and Discourse Examining Student Work

Estimation in Various Strands What strands of mathematic might we interweave estimation? Number, measurement, data, probability, etc. How do we help ourselves think integrationally rather than discretely when designing lessons?

Estimation Jars and Boxes What strategy did you use when you estimated each jar and box? Did the contents, shape or size of the box or jar affect your strategy? What questions do you have or what are you wondering about?

Data from the Jars How might you organize the data?

Is Mathematics An Exact Science? When is an approximate answer more useful than an exact answer? Talk to your neighbor and come up with situations when estimating is more appropriate/useful than finding an exact answer. Discuss situations in the world—not just personal uses of estimation.

When Do we Use Estimation? Make a list of situations in which we use estimation. Consider what methods we use to estimate. (e.g. mental mathematics; paper and pencil; calculator; formal equations as in statistics) Make a list of examples of when you personally use estimation and a list of when estimation is used in the world. On your list write down what tools you use (or think are used) to estimate for each situaiton.

SituationKind of AnswerMost Likely Method Planning a daily schedule SituationKind of AnswerMost Likely Method BudgetEstimateCalculator/P + P Money for Grocery shopping EstimateMental Time to get to airport EstimateMental TippingEstimateMental Comparing pricesEstimateMental Projected Profit How long it will take to accomplish a task Estimate Combination Mental People who will need a vaccination How much land is in the Sahara Desert Estimate Statistics Combination

Estimation Procedures Vary The mathematical procedures used in estimation range from making ball-park estimates, or guesstimates, through the various kinds of rounding (up, down or to the nearest multiple of a given number), to sophisticated procedures like those used in mathematical analysis, statistics, or economics. Example: The Dow Jones Industrial Average (30 stocks are used to determine economic trends) and the information is reported to the nearest tenth.

Estimates Are Easier to Use Than Accurate Numbers Answers derived from estimates maybe more reasonable and more realistic than those that attempt to be exact. Taxes—rounding to the nearest dollar does not impact the amount of money collected and saves the IRS time and money The projected cost of a trip is more easily estimated and likely to be more useful (especially if over- estimated) than trying to be exact

Estimates Can Provide Consistency The inflation rate for a given month is rounded to the nearest tenth of a percent The population of the world is rounded to the nearest hundred million (sometimes billion—7 billion present estimate)

Estimates are Useful When it is Impossible to Get an Exact Answer How many people come into New York City on a daily basis? How many people prefer Coca cola to Pepsi cola? Statistics is a branch of mathematics that relies on estimation through sampling and other means

Why teach estimation? What does estimation have to do with reasoning? What does estimation have to do with understanding our world? What does estimation have to do with the CCSS?

Eight CCSS Math Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

Construct Viable Arguments and Critique the Reasoning of Others Understand and use stated assumptions, definitions and previously established results Make and explore conjectures using a logical progression of statements Analyze arguments using cases, counterexamples, data, contexts Compare effectiveness of two plausible arguments Distinguish correct from flawed reasoning

Model with Mathematics Apply mathematics to solve everyday, society, and workplace problems Make assumptions and approximations to simplify a complicated situation and revise as needed Map quantitative relationships in situations using diagrams, charts, flow-charts, tables, etc. Analyze quantitative relationships to draw conclusions Interpret results in relation to the context determining whether answer makes sense or model needs revision

Class Clip ELL discussing the relationship between the factors of 24 and 48 “Math Congress”—Students are sharing their thinking and referring to the poster they created Teacher is working on developing language and ensuring that all students are engaging in meaning making 4 th grade

Focus How is this teacher generating discussion? What is the focus of her questions? What talk moves is she making to ensure that students are talking and listening to one another? What expectations is she setting and maintaining?

Student Work Share the samples of student work at your tables. There are six samples Each person should study one sample from the lens of “What does this student know?” Consider the student’s conjectures or attempts to generalize. Focus on reasoning and use a post-it to write down ONE question that might clarify, extend or refine the student’s thinking. Exchange the paper you worked on with a neighbor and discuss.