Big Idea 1 Grade 3

Welcome Trainer Introductions Housekeeping and Norms Restrooms, breaks/lunch, computer and phone use etiquette, sidebars Sign In Welcome/Trainer Introductions Housekeeping and Norms (i.e. restrooms, breaks/lunch, leaving early, questions, computer and phone use etiquette, sidebars, etc)

Participant Introductions Name, school, and interesting information you would like to share. How has math instruction changed? Participant Introductions – Name, School, and Interesting information they would like to share. Invite teachers to share the similarities and differences between the old and new concepts. Complete a K-W-L chart around Big Idea 1 Label chart paper or the white board with columns labeled K, W and L. Make sure each table has post-it notes and ask teachers to list what they know about Big Idea 1 on one post it, and what they would like to know about Big Idea 1 on another post it. Have teachers share their answers and place their notes on the chart.

K – W - L What do you KNOW about Big Idea 1 for grade 3? What do you WANT to KNOW about Big Idea 1 for grade 3?

Chapter 1 Preview Big Idea Project Chapter Planner Teaching for Depth Review Prerequisite Skills Developing Math Language Chapter 1 Preview – Trainers introduce the TE for chapter 1 by discussing the Big Idea Project at the beginning of the chapter, the chapter planner, Teaching for Depth, Review Prerequisite Skills and Developing Math Language. The components appear at the beginning of each chapter.

Collaboration ! Work in small groups to review the following sections for each lesson in chapter 5. About the Math Differentiated Instruction Common Errors Have teachers work in small groups to review the following sections for each lesson in chapter 1. They will share out with the rest of the group. Example: One team will be assigned About the Math, Differentiated Instruction and Common Errors for lesson 1, another team will work on the same sections for lesson 2 and so on. Note: The trainer will separate the participants into groups and assign the sections accordingly.

Take a Break 10 minute break See you in 10 minutes

Comparing the Standards Grade Level Number of Old GLE’s Number of New Benchmarks K 67 11 1st 78 14 2nd 84 21 3rd 88 17 4th 89 5th 77 23 6th 19 7th 22 8th 93 Old average of 83 GLEs vs new average of 19 Benchmarks per grade. We were teaching a mile wide and an inch deep, teachers were doing what we asked them to do, cover lots of content – drive by teaching—skimming the surface. Old average of 83 GLEs to new average of 19 Benchmarks per grade

How Will Instruction Change? Fewer topics per grade due to less repetition from year to year. Move from “covering” topics to teaching them in-depth for long term learning. Individual teachers will need to know how to begin each topic at the concrete level, move to the abstract, and connect it to more complex topics. Teaching to depth of understanding requires that children experience concepts in multiple representations—composing and decomposing numbers and operations. Focus on the “why” as well as the “how”. Caution them to avoid premature exposure to algorithms and procedures. These can not be taught until depth of knowledge is established otherwise procedures are learned without understanding and easily forgotten.

Terms in the 1996 and 2007 Standards Grade Band Strand Benchmark Grade Level Expectation 2007 Body of Knowledge Standard Benchmark Supporting Idea Big Idea Depth of Knowledge Rating Old vs. New: Standards are no longer “grade-banded” (K-2) (3-5). Benchmarks are coded so that they are grade specific. No need for GLEs.

Structure of the Standards K-8 Grade Level -Big Ideas/Supporting Ideas -Benchmarks 9-12 Body of Knowledge -Standards Supporting ideas are equally important.

What is a Supporting Idea? Supporting Ideas are not subordinate to Big Ideas Supporting Ideas may serve to prepare students for concepts or topics that will arise in later grades Supporting Ideas may contain grade-level appropriate math concepts that are not included in the Big Ideas There are 3 Big Ideas per grade level. However, the number of supporting ideas vary from grade level to grade level.

Big Idea/ Supporting Idea Coding Schema MA. 5. A. 3. 1 Subject Grade-Level Body of Knowledge Big Idea/ Supporting Idea Benchmark MA. 912. G. 3. 1 Subject Grade-Level Body of Knowledge Standard Benchmark Note: MA still represents Math. Next number is the actual grade level for the content. Next letter represents the Body of Knowledge (in this case A for Algebra that will also include Number and Operations. G stands for Geometry and Measurement. S is for Statistics or rather Data Analysis in elementary.

Where to Find the 2007 Standards Document www.floridastandards.org www.fldoestem.org STEM = Science, Technology, Engineering, and Mathematics

Next Generation Math Standards Grade 3 BIG IDEA 1: Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts.

MA.3.A.1.1 Model multiplication and division including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement, and partitioning. MA.3.A.1.2 Solve multiplication and division fact problems by using strategies that result from applying number properties. MA.3.A.1.3 Identify, describe, and apply division and multiplication as inverse operations. MA. 3.A.1.1 Explain meaning of multiplicative comparison as Jo has 2 pencils. I have 3 times as many. How many do I have? Measurement and partitioning are 2 division situations. Measurement: 45 cards –5 go into each box. How many boxes? Partitioning—45 cards to share with 5 . How many does each get? MA.3.A.1.2 Do not have to id properties by name. Must understand use e.g. 14 x 3 = 10 x 3 + 4 x 3

BIG IDEA 2: Big IDEA 2 Develop an understanding of fractions and fraction equivalence. MA.3.A.2.1 Represent fractions, including fractions greater than one, using area, set, and linear models. MA.3.A.2.2 Describe how the size of the fractional part is related to the number of equal sized pieces in the whole. MA.3.A.2.1 –“Fractions greater than one” is the name used for improper fractions. Identify through graphic representation and not procedure. Equal number of fraction questions for area, set and linear models on FCAT. MA.3.A.2.2 - For instance, "As the number of equal parts increases, the size of each fractional part decreases." Fractions can also be compared by looking at numerators, such as when comparing 1/5 and 1/6. Since both fractions represent one part of a whole, the size of the parts can be compared.

MA.3.A.2.3 Compare and order fractions, including fractions greater than one, using models and strategies. MA.3.A.2.4 Use models to represent equivalent fractions, including fractions greater than 1, and identify representations of equivalence. MA.3.A.2.3 – Do not teach finding common denominators or cross multiplying to compare!!!!! Children should use strategies to reason: benchmarks of half, close to zero, close to whole, comparing numerators when denominator are the same or comparing denominators when numerators are the same. MA.3.A.2.4 – Children will use models and not procedures to find equivalent fractions.

Big IDEA 3 Describe and analyze properties of two-dimensional shapes. MA.3.G.3.1 Describe, analyze, compare, and classify two- dimensional shapes using sides and angles - including acute, obtuse, and right angles - and connect these ideas to the definition of shapes. Students will be assessed on regular polygons (equal sides and angles) and irregular polygons with 3,4,5,6,8,10 sides. Angles will not be assessed in isolation.

MA.3.G.3.2 Compose, decompose, and transform polygons to make other polygons, including concave and convex polygons with three, four, five, six, eight, or ten sides. MA.3.G.3.3 Build, draw, and analyze two-dimensional shapes from several orientations in order to examine and apply congruence and symmetry. MA.3.G.3.2 With pattern blocks, a trapezoid and a triangle can be combined to form a parallelogram or a large triangle. Also, the hexagon can be decomposed to form two trapezoids, and so forth. Or one can cut a triangle off of a parallelogram so that, when translated and attached to the other side, the parallelogram becomes a rectangle. MA.3.G.3.3 – Remind them that children have not heard of congruence or symmetry in previous grades.

Supporting Idea 4 Algebra MA.3.A.4.1 Create, analyze, and represent patterns and relationships using words, variables, tables, and graphs. MA.3.A.4.1 Old FCAT - students need to find next missing element. New FCAT - students are asked to extend pattern beyond next element . Rules for numeric patterns and relationships shown in function tables must include only one operation limited to addition, subtraction, or multiplication not division.

Supporting Idea 5 Geometry and Measurement MA.3.G.5.1 Select appropriate units, strategies, and tools to solve problems involving perimeter. MA.3.G.5.2 Measure objects using fractional parts of linear units such as 1/2, 1/4, and 1/10. MA.3.G.5.3 Tell time to the nearest minute and to the nearest quarter hour, and determine the amount of time elapsed MA.3.G.5.1 – Area is no longer 3rd grade curriculum….it was moved to 4th grade, surface area moved to 5th grade. 3rd grade focuses on perimeter of 3, 4, 5, 6, 8, or 10 sided polygon or composed of composite rectangles. NOT JUST RECTANGLES AS IN PAST. May have to measure sides using a ruler to find perimeter on FCAT. MA.3.G.5.2 – Measure using a ruler to nearest ½ and ¼ in. (ruler is divided into16ths) or to nearest centimeter or mm. -- NO CONVERSIONS MA.3.G.5.3 – Tell time to nearest minute or quarter hour—Only learned hour and half hour in grade 2. Elapsed time could be in increments of quarter hour and 5 minutes, for time less than 1 hour or hour and half hour for time more than 1 hour but less than 24 hours.

Supporting Idea 6 Number and Operations MA.3.A.6.1 Represent, compute, estimate, and solve problems using numbers through hundred thousands. MA.3.A.6.2 Solve non-routine problems by making a table, chart, or list and searching for patterns. MA.3.A.6.1 – Inequality symbols, equal, not equal, greater than and less than will be used—front end estimation will not be an acceptable form of estimation. MA.3.A.6.2 Some examples: Show 5 different combinations of US coins that total 53¢. The 24 chairs in the classroom are arranged in rows with the same number of chairs in each row. List all of the possible ways the chairs can be arranged.

Supporting Idea 7 Data Analysis MA.3.S.7.1 Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments. Line graphs are NOT assessed at this level. Remind them that graphing has not been formally taught in k-2. If primary teachers did not expose children to graphing, then this may be the first time that they are experiencing it.