Everyday Mathematics ® Common Core Instructional Planning and Pacing Guide 2 Grade Introduction The Everyday Mathematics® Common Core Instructional Planning and Pacing Guide provides in‐depth information supporting the lesson objectives, the Common Core State Standards (CCSS)—both content and practices—and the need to review and maintain skills and concepts. This guide also provides instruction necessary to develop prerequisite skills that will impact future instruction. This guide may be used as a complement to the pacing recommended in your Teacher’s Lesson Guide Unit Organizers and on the grade‐level specific Content by Strand Poster. The needs of your students will dictate the pace of your lessons as will the amount of time for mathematics instruction allocated by your school or district. The information provided also reflects the depth to which the CCSS are covered, while maintaining the integrity of the instructional focus of Everyday Mathematics. When utilizing this guide, note that only specific portions of a lesson are labeled with the CCSS Content Standards. While all portions of the three‐part lesson are important, the intent is to provide you, the teacher, with important information on: 1) the alignment of various portions of the lesson to specific content standards 2) the Math Box problems and Games where important review opportunities are presented, as described by the label Maintain 3) the Math Box problems and Games where essential prerequisite skills are presented that will impact instruction both within your grade and in subsequent grade levels, as described by the label Foundation The detailed information provided in this guide is yet another step in communicating with Everyday Mathematics educators and supporting instruction, planning and delivery of the Common Core State Standards within Everyday Mathematics curriculum. We hope you will find this chart to be a relevant tool in the planning and pacing of your lessons as well as a valuable tool in delivering all that you need to meet and exceed the Common Core State Standards. Copyright © 2012 by The McGraw‐Hill Companies, Inc. All rights reserved. The contents, or parts thereof, may be reproduced for use with Everyday Mathematics, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw‐Hill Companies, Inc., including, but not limited to network storage or transmission, or broadcast for distance learning. Send all inquiries to: McGraw‐Hill Education STEM Learning Solutions Center P.O. Box 812960 Chicago, IL 60681 Grade 2 Contents Unit 1 ………………………………………………………………………………………………………………………………………………………………. 1 Unit 2 ………………………………………………………………………………………………………………………………………………………………. 4 Unit 3 ………………………………………………………………………………………………………………………………………………………………. 8 Unit 4 ………………………………………………………………………………………………………………………………………………………………. 11 Unit 5 ………………………………………………………………………………………………………………………………………………………………. 14 Unit 6 ………………………………………………………………………………………………………………………………………………………………. 17 Unit 7 ………………………………………………………………………………………………………………………………………………………………. 21 Unit 8 ………………………………………………………………………………………………………………………………………………………………. 24 Unit 9 ………………………………………………………………………………………………………………………………………………………………. 26 Unit 10 ………………………………………………………………………………………………………………………………………………………….… 29 Unit 11 ………………………………………………………………………………………………………………………………………………………….… 32 Unit 12 ………………………………………………………………………………………………………………………………………………………….… 35 Common Core Content Standards for Grade 2 ………………………………………………………………………………………….….… 37 Standards for Mathematical Practice ………………………………………………………………………………………………….…………… 40 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. iii Unit 1 Copyright © The McGraw‐Hill Companies, Inc. Numbers and Routines Weeks 1–4 (Lessons 11–113) CCSS Lesson 11 12 13 14 15 Title/Objective Focus Math Message and Number Sequences To introduce the Math Message routine; and to review number sequences and number lines. Tools and Coins To introduce the tool kits; and to guide children as they find the values of coin combinations. Calendars and Clocks To review months, weeks, and days; and to review telling time. Partner Study Routines To provide practice with addition facts; and to establish partnership principles. Grouping by Tens—$1, $10, $100 To provide review for grouping by tens; and to provide practice for exchanging $1, $10, and $100 bills. Common Core State Standards* Part 1: Introduces the Math Message routine and reviews writing number sequences on a number line. [2.NBT.1, 2.NBT.1a, 2.NBT.2, 2.NBT.3, 2.MD.6] Part 3: Readiness Playing Number-Line Squeeze [2.NBT.4] SMP1, 2, 4, 6, 7; 2.NBT.1, 2.NBT.1a, 2.NBT.2, 2.NBT.3, 2.MD.6 Getting Started: Mental Math and Reflexes [2.NBT.2] Part 1: Introduces tools used throughout the entire year and focuses on finding the total value of coins. [2.NBT.2] Part 3: Extra Practice [2.NBT.2] SMP2–4, 6, 7; 2.NBT.2 Part 1: Reviews months, weeks, and days, and provides practice telling and writing time to the nearest 5 minutes. [2.MD.7] Part 3: Enrichment and ELL Support [2.MD.7] SMP2–7; 2.MD.7 Part 1: Focuses on modeling partnership principles and practicing addition facts by playing Addition Top-It. [2.OA.2] Part 3: Readiness Playing Addition Top-It [2.OA.2]; Enrichment Playing Coin Top-It [2.MD.8] SMP2, 5–7; 2.OA.2 Getting Started: Mental Math and Reflexes [2.NBT.2]; Math Message [2.MD.8] Part 1: Focuses on grouping by tens using money. [2.NBT.1, 2.NBT.2, 2.MD.8] Part 2: Game: Money Exchange Game [2.MD.8] or Addition Top-It [2.OA.2] Part 3: Readiness Playing Penny-Nickel Exchange [2.MD.8] SMP2, 4, 6, 7; 2.NBT.1, 2.NBT.2, 2.MD.8 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 1 Copyright © The McGraw‐Hill Companies, Inc. Math Boxes 16 To introduce My Reference Book; and to introduce the Math Boxes routine. Working in Small Groups To establish rules for working in small groups; and to review number patterns and sequences. 17 Number Grids To guide children as they explore place-value patterns on number grids. 18 Equivalent Names for Numbers 19 To provide experiences with giving equivalent names for numbers; and to review calculator use. Part 1: Introduces the Math Boxes routine and My Reference Book which will be used in future lessons. [2.MD.8] Math Boxes: [ 1-6]; 1 [2.NBT.2, 2.NBT.8]; 2 [2.NBT.5]; 3 [Foundation]; 4 [2.OA.2]; 5 [2.G.1]; 6 [2.OA.3] Part 2: Game: Penny Plate [2.OA.2] Part 3: Readiness Playing Two-Fisted Penny Addition [2.OA.2]; Extra Practice [2.OA.2] Getting Started: Math Message [2.NBT.2] Part 1: Focuses on modeling small group principles and reading and writing numbers within 1,000. [2.NBT.2, 2.NBT.3] Part 2: Game: Addition Top-It [2.OA.2] Math Boxes: [ 1-7↔1-9↔1-11]; 1 [2.MD.8]; 2 [Foundation]; 3 [2.NBT.4]; 4 [2.MD.7]; 5 [2.NBT.7, 2.NBT.9]; 6 [2.NBT.2] Writing/Reasoning: [2.NBT.2] Part 3: Readiness and Extra Practice [2.NBT.2] Getting Started: Mental Math and Reflexes [2.OA.2, 2.NBT.2]; Math Message [2.NBT.2] Part 1: Focuses on how place value is displayed on number grids and on solving number grid puzzles. [2.NBT.2, 2.NBT.8] Part 2: Game: Number-Grid Game [2.NBT.2] Math Boxes: [ 1-8↔1-10↔1-12]; 1, 2 [2.NBT.2, 2.NBT.8]; 3 [2.MD.8]; 4 [2.OA.3]; 5 [2.NBT.2]; 6 [2.OA.2] Part 3: Readiness and Enrichment [2.NBT.2] Part 1: Focuses on how to use a calculator and provides practice finding equivalent names for numbers. [2.NBT.2] Part 2: Solving Hundreds-Tens-and-Ones Problems: [2.NBT.1, 2.MD.8] Math Boxes: [ 1-9↔1-7↔1-11]; 1 [2.MD.8]; 2, 6; 3 [2.NBT.4]; 4 [2.MD.7]; 5 [2.NBT.7, 2.NBT.9] Part 3 Enrichment [2.NBT.1] SMP2, 4, 6, 7; 2.OA.2, 2.MD.8 SMP2, 3, 5–7; 2.NBT.2, 2.NBT.3 SMP1, 5–7; 2.OA.2; 2.NBT.2, 2.NBT.8 SMP1, 2, 4–7; 2.NBT.1, 2.NBT.2, 2.MD.8 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 2 110 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.NBT.1] Math Counting Patterns To guide children as they count and look for patterns on the calculator. Relations (<, >, =) and Home Links To provide experiences with comparing numbers using the relation symbols <, >, and =; and to introduce Home Links. 111 112 113 EXPLORATIONS: Exploring Temperatures, Base-10 Structures, and Dominoes To guide children as they read and display temperatures; combine values of ones, tens, and hundreds using base-10 blocks; and explore addition facts on dominoes. Progress Check 1 To assess children’s progress on mathematical content through the end of Unit 1. Message [2.NBT.2] Part 1: Focuses on finding patterns while counting on a calculator. [2.OA.3, 2.NBT.2] Part 2: Math Boxes: [ 1-10↔1-8↔1-12]; 1 [2.NBT.2, 2.NBT.8]; 2 [2.NBT.4]; 3 [2.MD.8]; 4 [2.OA.3]; 5 [2.NBT.2]; 6 [2.OA.2] Part 3: Readiness [2.OA.3]; Enrichment [2.NBT.2] Getting Started: Mental Math and Reflexes [2.NBT.4]; Math Message [2.NBT.4] Part 1: Reviews relation symbols and provides practice using them to compare numbers; introduces Home links. [2.NBT.4] Part 2: Game: Addition Top-It [2.OA.2] Math Boxes: [ 1-11↔1-7↔1-9]; 1 [2.MD.8]; 2 [Foundation]; 3 [2.NBT.4]; 4 [2.MD.7]; 5 [2.NBT.8]; 6 [2.NBT.7] Home Link: [2.OA.4] Part 3: Enrichment Playing Number Top-It (5-Digit Numbers) [2.NBT.4] Getting Started: Mental Math and Reflexes [2.NBT.2] Part 1: Focuses on understanding temperature; understanding place value with 3-digit numbers; and developing fluency with addition facts. [2.OA.3, 2.NBT.1a, 2.NBT.3] Part 2: Game: Addition Top-It [2.OA.2] Math Boxes: [ 1-12↔1-8↔1-10]; 1 [2.NBT.2, 2.NBT.8]; 2 [2.NBT.4]; 3 [2.MD.8]; 4 [2.OA.3]; 5 [2.OA.2]; 6 [2.OA.2] Writing/Reasoning: [2.OA.3] SMP1, 3, 5–7; 2.OA.3, 2.NBT.1, 2.NBT.2 SMP2, 5–7; 2.OA.2, 2.NBT.4 SMP1–6; 2.OA.3, 2.NBT.1a, 2.NBT.2, 2.NBT.3 Part 1: Checks children’s progress at the end of Unit 1. Part 2: Math Boxes: [ 1-13↔Unit 2]; 1 [2.NBT.3]; 2 [2.OA.2]; 3 [2.NBT.2]; 4 [2.NBT.7]; 5 [2.NBT.2]; 6 [2.OA.2] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 3 Unit 2 Copyright © The McGraw‐Hill Companies, Inc. Addition and Subtraction Facts Weeks 4–7 (Lessons 21–214) CCSS Lesson Title/Objective Addition Number Stories To guide children as they make up, represent, and solve addition number stories. 21 Review “Easy” Addition Facts 22 To review +0 and +1 addition facts; and to provide practice with addition facts in which one of the addends is 0, 1, 2, or 3. Focus Doubles Facts To review and provide practice for doubles facts. 23 Common Core State Standards* Getting Started: Math Message [2.OA.1] Part 1: Focuses on using addition strategies to solve number stories. [2.OA.1, 2.MD.6] Part 2: Completing Number-Grid Puzzles: [2.NBT.8] Math Boxes: [ 2-1↔2-3]; 1 [2.OA.1]; 2 [2.NBT.7, 2.NBT.9]; 3 [2.NBT.2]; 4 [2.OA.2]; 5 [2.MD.7]; 6 [2.MD.8] Home Link: [2.OA.1] Part 3: Readiness and Enrichment [2.OA.1] Getting Started: Mental Math and Reflexes [2.OA.1]; Math Message [2.NBT.9]; Home Link 2-1 Follow-Up [2.OA.1] Part 1: Reviews and practices addition strategies for adding quickly within 20. [2.OA.1, 2.OA.2, 2.NBT.9] Part 2: Math Boxes: [ 2-2↔2-4]; 1, 2 [2.NBT.2]; 3 [2.OA.2]; 4 [2.MD.8]; 5 [2.MD.10]; 6 [2.NBT.5] Home Link: [2.OA.2] Part 3: Readiness Domino Top-It [2.OA.2]; Enrichment [2.OA.1] Getting Started: Mental Math and Reflexes [2.OA.2]; Math Message [2.OA.3] Part 1: Reviews and practices the doubles strategy for adding quickly within 20. [2.OA.2, 2.OA.3, 2.NBT.9] Part 2: Game: Doubles or Nothing [2.OA.2] Math Boxes: [ 2-3↔2-1]; 1 [2.OA.1]; 2 [2.NBT.7, 2.NBT.9]; 3 [2.NBT.2]; 4 [2.OA.2]; 5 [2.MD.7]; 6 [2.MD.8] Home Link: [2.OA.2] Part 3: Readiness and Extra Practice [2.OA.2] SMP1–5, 7; 2.OA.1, 2.NBT.8, 2.MD.6 SMP2, 3, 5–8; 2.OA.1, 2.OA.2, 2.NBT.9 SMP5–7; 2.OA.2, 2.OA.3, 2.NBT.9 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 4 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Math Message [2.OA.2] Home Link Follow-Up Turn-Around Facts and the +9 [2.OA.3] Shortcut 24 To review the turn-around shortcut for addition; and to discover and provide practice for a shortcut for addition facts that have 9 as an addend. Addition Strategies That Use Doubles Facts 25 To provide opportunities for children to explore and practice doubles-plus-1 and doubles-plus-2 facts. Subtraction from Addition To review the –0 and –1 shortcuts; and to guide children to identify the subtraction facts related to given addition facts. 26 Part 1: Focuses on reviewing addition strategies for basic addition facts. [2.OA.2, 2.OA.3] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 2-4↔2-2]; 1 [2.NBT.2]; 2 [2.NBT.8]; 3, 6 [2.NBT.5]; 4 [2.MD.8]; 5 [2.MD.10] Home Link: [2.OA.2] Part 3: Readiness and Extra Practice [2.OA.2] Getting Started: Mental Math and Reflexes [2.OA.2]; Math Message [2.OA.2] Part 1: Focuses on practicing addition strategies using doubles facts to add quickly within 20. [2.OA.2, 2.OA.3, 2.NBT.9] Part 2: Game: Domino Top-It [2.OA.2] Math Boxes: [ 2-5↔2-7]; 1 [2.G.1]; 2 [2.MD.7]; 3 [2.OA.2]; 4 [Foundation]; 5 [2.NBT.4]; 6 [2.MD.7] Home Link: [2.OA.2] Part 3: Readiness [2.OA.2, 2.OA.3]; Enrichment [2.OA.2] Getting Started: Mental Math and Reflexes [2.OA.2];Math Message [2.OA.1] Part 1: Focuses on understanding how subtraction is related to addition and discusses subtraction shortcuts. [2.OA.1, 2.OA.2, 2.NBT.9, 2.MD.6] Part 2: Game: Addition Top-It [2.OA.2], Subtraction Top-It [2.OA.2] Math Boxes: [ 2-6↔2-8]; 1 [2.NBT.2, 2.NBT.8]; 2 [Maintain]; 3 [2.OA.2]; 4 [2.NBT.4]; 5 [2.NBT.5]; 6 [2.MD.7] Home Link: [2.OA.2] Part 3: Readiness and Enrichment [2.OA.2; 2.NBT.9] SMP5–8; 2.OA.2, 2.OA.3 SMP2, 5, 6, 8; 2.OA.2, 2.OA.3, 2.NBT.9 SMP2, 4–6, 8; 2.OA.1, 2.OA.2, 2.NBT.9, 2.MD.6 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 5 Copyright © The McGraw‐Hill Companies, Inc. Fact Families 27 To demonstrate the inverse relationship between addition and subtraction; and to provide practice for addition and subtraction facts for sums up to and including 10. EXPLORATIONS: Exploring Weights and Scales, Odd and Even Patterns, and Equal Groups 28 29 To guide children as they explore weight using a pan balance and spring scale, investigate odd and even patterns, and find the total number of objects in equal groups. Name Collections To review the concept that a number can be named in many ways. Frames-and-Arrows Routines 210 To guide children as they use a given addition or subtraction rule to generate a number sequence, and as they identify the rule for a given number sequence. Getting Started: Mental Math and Reflexes [2.OA.2] Part 1: Discusses how subtraction relates to addition and uses fact triangles to demonstrate fact families. [2.OA.2, 2.NBT.9] Part 2: Math Boxes: [ 2-7↔2-5]; 1 [2.G.1]; 2 [2.MD.7]; 3 [2.OA.2]; 4 [Foundation]; 5 [2.NBT.4]; 6 [2.MD.7] Writing/Reasoning: [2.OA.2, 2.NBT.9] Home Link: [2.OA.2] Part 3: Readiness, Enrichment, and ELL Support [2.OA.2] SMP2, 3, 5, 6, 8; 2.OA.2, 2.NBT.9 Getting Started: Mental Math and Reflexes [2.OA.2] Part 1: Focuses on using tools to explore weight, adding odd and even numbers, and making equal groups. [2.OA.3] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 2-8↔2-6]; 1 [2.NBT.2]; 2 [Maintain]; 3 [2.NBT.8]; 4 [2.NBT.4]; 5 [2.NBT.5]; 6 [2.MD.7] SMP1, 2, 4–8; Part 1: Reviews how numbers can be named many different ways; introduces the facts-practice game Name That Number. [2.NBT.3] Part 2: Math Boxes: [ 2-9↔2-11↔2-13]; 1 [2.MD.8]; 2 [2.MD.7]; 3 [2.OA.2]; 4 [2.NBT.4]; 5 [2.G.1]; 6 [2.MD.10] SMP1, 2, 5–7 2.OA.2, 2.OA.3 Getting Started: Mental Math and Reflexes [2.NBT.2] Part 1: Review and practice Frame-and-Arrow problems to practice addition and subtraction. [2.NBT.2] Part 2: Game: Name That Number [2.NBT.3] Math Boxes: [ 2-10↔2-12]; 1, 2, 3, 4 [2.OA.2]; 5 [2.MD.8]; 6 [2.NBT.5] Home Link: [2.NBT.2] Part 3: Readiness and Enrichment [2.NBT.2] SMP1, 2, 5–8; 2.NBT.2 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 6 211 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.NBT.8]; Math “What’s My Rule?” Routines To provide experiences with identifying missing numbers in number pairs that are generated by a rule, and determining the rule used to generate number pairs. Counting Strategies for Subtraction To review, develop, and provide practice for subtraction strategies. 212 213 Shortcuts for “Harder” Subtraction Facts To guide children as they discover and practice shortcuts for subtracting 9 or 8 from any number. Progress Check 2 214 To assess children’s progress on mathematical content through the end of Unit 2. Message [2.OA.1] Part 1: Reviews “What’s My Rule?” routines to practice addition and subtraction. [2.OA.1, 2.OA.2] Part 2: Math Boxes: [ 2-11↔2-9↔2-13]; 1 [2.MD.8]; 2 [2.MD.7]; 3 [2.OA.2]; 4 [2.NBT.4]; 5 [2.G.1]; 6 [2.MD.10] Home Link: [2.OA.2] SMP1, 2, 4–8; 2.OA.1, 2.OA.2, 2.NBT.8 Getting Started: Mental Math and Reflexes [2.NBT.2, 2.NBT.8] Part 1: Focuses on reviewing and practicing strategies to subtract quickly within 100. [2.OA.2, 2.NBT.9] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 2-12↔2-10]; 1 [2.NBT.7, 2.NBT.9]; 2, 3 [2.OA.2]; 4 [2.NBT.7]; 5 [2.MD.8]; 6 [2.NBT.5] Writing/Reasoning: [2.NBT.9] Home Link: [2.OA.2] Part 3: Readiness Playing the Difference Game and Enrichment Playing the Number-Grid Difference Game [2.NBT.5]; Extra Practice [2.OA.2] Getting Started: Mental Math and Reflexes [2.OA.2] Part 1: Introduces strategies and shortcuts for subtracting within 100. [2.OA.2, 2.NBT.9] Part 2: Math Boxes: [ 2-13↔2-9↔2-11]; 1 [2.MD.8]; 2 [2.MD.7]; 3 [2.OA.2]; 4 [2.NBT.4]; 5 [2.G.1]; 6 [2.MD.10] Home Link: [2.OA.2] Part 3: Readiness and Extra Practice [2.OA.2] Part 1: Checks children’s progress at the end of Unit 2. Part 2: Math Boxes: [ 2-14↔Unit 3]; 1 [2.MD.10]; 2 [Maintain]; 3 [2.NBT.5]; 4 [2.MD.7]; 5 [2.MD.8]; 6 [2.NBT.5] SMP1, 2, 4–7; 2.OA.2, 2.NBT.2, 2.NBT.8, 2.NBT.9 SMP2, 4–8; 2.OA.2, 2.NBT.9 * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 7 Unit 3 Copyright © The McGraw‐Hill Companies, Inc. Place Value, Money, and Time Weeks 7–9 (Lessons 31–39) CCSS Lesson Title/Objective Numeration and Place Value To review place value in 2-digit and 3-digit numbers. 31 Using Coins to Buy Things To review coin values and exchanges among coins; and to provide experiences with finding coin combinations needed to pay for items. 32 Focus Telling Time 33 To review telling time; and to provide experiences with writing time in digital-clock notation. Common Core State Standards* Getting Started: Math Message [2.NBT.1] Part 1: Focuses on understanding place value in 2- and 3-digit numbers. [2.NBT.1, 2.NBT.1a, 2.NBT.3, 2.NBT.4] Part 2: Game: Digit Game [2.NBT.3] Math Boxes: [ 3-1↔3-3]; 1, 2 [2.NBT.5]; 3 [2.NBT.8]; 4, 5 [2.MD.8]; 6 [2.NBT.5] Home Link: [2.NBT.1, 2.NBT.1a, 2.NBT.3] Part 3: Readiness [2.NBT.2]; Enrichment [2.NBT.1, 2.NBT.3] Getting Started: Mental Math and Reflexes [2.NBT.2]; Math Message [2.MD.8] Part 1: Focuses on solving problems involving exchanging coins. [2.MD.8] Part 2: Game: Spinning for Money [2.MD.8] Math Boxes: [ 3-2↔3-4]; 1 [2.MD.7]; 2 [2.OA.3]; 3 [2.NBT.4]; 4 [2.MD.10]; 5 [Maintain]; 6 [2.MD.8] Home Link: [2.MD.8] Part 3: Readiness Playing Penny-Nickel Exchange or PennyNickel-Dime Exchange [2.MD.8]; Enrichment [2.MD.5] Getting Started: Math Message [2.MD.7] Part 1: Focuses on telling and writing time in analog and digital notation. [2.MD.7] Part 2: Practicing with +, – Fact Triangles: [2.OA.2] Math Boxes: [ 3-3↔3-1]; 1 [2.NBT.5]; 2 [2.OA.2]; 3 [2.NBT.8]; 4 [2.MD.8]; 5 [2.OA.1]; 6 [2.NBT.6] Home Link: [2.MD.7] Part 3: Readiness and Enrichment [2.MD.7] SMP1–3, 5–7; 2.NBT.1, 2.NBT.1a, 2.NBT.2, 2.NBT.3, 2.NBT.4 SMP1–7; 2.NBT.2, 2.MD.8 SMP2, 4, 5, 6; 2.OA.2, 2.MD.7 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 8 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Math Message [2.NBT.3] EXPLORATIONS: Exploring Part 1: Focuses on understanding place value, telling and Numbers, Time, and Geoboards 34 To provide experiences with representing and renaming numbers with base-10 blocks; reviewing time; and making, describing, and comparing geoboard shapes. Data Day: Pockets To provide experiences with gathering data, entering data in a table, and drawing a bar graph and picture graph; and to demonstrate a strategy for finding the middle value in a data set. 35 Frames-and-Arrows Having Two Rules 36 To guide children as they solve Frames-andArrows problems having two rules. Making Change by Counting Up To guide children as they make change by counting up from the cost of an item to the amount tendered. 37 writing time, and making shapes. [2.NBT.3, 2.G.1] Part 2: Math Boxes: [ 3-4↔3-2]; 1 [2.MD.7]; 2 [2.OA.3]; 3 [2.NBT.4]; 4 [2.MD.10]; 5 [Maintain]; 6 [2.MD.8] Part 3: Readiness Playing Base-10 Exchange [2.NBT.5] SMP1–3, 5–7; 2.NBT.3, 2.G.1 Part 1: Focuses on representing and interpreting data on a bar graph and picture graph. [2.MD.10] Part 2: Math Boxes: [ 3-5↔3-7]; 1 [2.NBT.4]; 2 [2.MD.8]; 3 [2.OA.2]; 4 [2.NBT.8]; 5 [2.OA.1]; 6 [Maintain] Home Link: [2.MD.10] Part 3: Enrichment [2.MD.10] Getting Started: Mental Math and Reflexes [2.OA.1]; Math Message [2.OA.1] Part 1: Focuses on using addition and subtraction to solve Frames-and-Arrows problems having two rules. [2.OA.1] Part 2: Game: Dollar Rummy [2.MD.8] Math Boxes: [ 3-6↔3-8]; 1 [2.MD.8]; 2 [2.NBT.5]; 3 [2.MD.10]; 4 [Foundation]; 5 [2.OA.1]; 6 [2.NBT.8] Part 3: Readiness [2.MD.6] Getting Started: Mental Math and Reflexes [2.NBT.2]; Math Message [2.MD.8] Part 1: Focuses on counting up as a strategy for subtraction. [2.OA.1, 2.MD.8] Part 2: Game: Digit Game [2.NBT.1, 2.NBT.1a, 2.NBT.3] Math Boxes: [ 3-7↔3-5]; 1 [2.NBT.4]; 2 [2.MD.8]; 3 [2.NBT.5]; 4 [2.NBT.8]; 5 [2.OA.1]; 6 [Maintain] Writing/Reasoning: [2.NBT.1] Home Link: [2.OA.1, 2.MD.8] Part 3: Readiness Playing High Roller [2.NBT.2, 2.NBT.4]; Enrichment [2.MD.8] SMP1, 2, 4, 6–8; 2.MD.10 SMP1, 3, 6–8; 2.OA.1, 2.MD.6 SMP1–7; 2.OA.1, 2.NBT.1, 2.NBT.1a, 2.NBT.2, 2.MD.8 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 9 38 Copyright © The McGraw‐Hill Companies, Inc. Coin Exchanges To guide children as they solve multistep problems for amounts under $1.00; and as they practice making change using nickels, dimes, and quarters. Progress Check 3 39 To assess children’s progress on mathematical content through the end of Unit 3. Getting Started: Mental Math and Reflexes [2.MD.8]; Home Link Follow-Up [2.MD.8] Part 1: Focuses on extending understanding of coin exchanges and making change. [2.OA.1, 2.MD.8] Part 2: Practice Making Change [2.OA.1, 2.MD.8] Math Boxes: [ 3-8↔3-6]; 1 [2.MD.8]; 2 [2.NBT.5]; 3 [2.MD.10]; 4 [Foundation]; 5 [2.OA.1]; 6 [2.NBT.8] Writing/Reasoning: [2.OA.1] Home Link: [2.MD.8] Part 3: Enrichment [2.MD.8]; Extra Practice [2.MD.8] SMP2, 4, 6; 2.OA.1, 2.MD.8 Part 1: Checks children’s progress at the end of Unit 3. Part 2: Math Boxes: [ 3-9↔Unit 4]; 1, 2 [2.OA.1]; 3 [2.MD.8]; 4 [Maintain]; 5 [2.NBT.5]; 6 [2.NBT.8] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 10 Unit 4 Copyright © The McGraw‐Hill Companies, Inc. Addition and Subtraction Weeks 10–12 (Lessons 41–410) CCSS Lesson 41 Title/Objective Focus Change-to-More Number Stories To guide children as they solve change-to-more number stories. Parts-and Total Number Stories To guide children as they solve parts-and-total number stories. 42 43 EXPLORATIONS: Exploring Temperature, Money, and Shapes To guide children as they explore reading temperatures on a thermometer, practice finding the total value of a group of coins, and develop readiness for classifying geometric shapes. Temperature Changes 44 To guide children as they read and show temperatures and solve number stories about temperature changes. Common Core State Standards* Part 1: Focuses on practicing addition strategies to solve number stories. [2.OA.1] Part 2: Math Boxes: [ 4-1↔4-3]; 1 [2.OA.2]; 2 [2.MD.7]; 3 [2.NBT.8]; 4 [2.MD.8]; 5 [2.NBT.4]; 6 [2.G.1] Home Link: [2.OA.1] Part 3: Enrichment [2.OA.1] Getting Started: Mental Math and Reflexes [2.MD.8]; Math Message [2.OA.1, 2.MD.8] Part 1: Focuses on practicing addition strategies to solve number stories. [2.OA.1, 2.NBT.5, 2.MD.6, 2.MD.8] Part 2: Game: Addition Spin [2.NBT.5] Math Boxes: [ 4-2↔4-4]; 1 [2.NBT.8]; 2, 4 [2.MD.8]; 3 [2.NBT.4]; 5 [2.OA.2]; 6 [2.G.1] Home Link: [2.OA.1, 2.NBT.5] Part 3: Readiness [2.OA.1, 2.NBT.5, 2.MD.8]; Enrichment [2.OA.1, 2.NBT.5] Part 1: Focuses on reading temperatures, solving money number stories, and recognizing attributes of shapes. [2.MD.8, 2.G.1] Part 2: Practicing with +, – Fact Triangles: [2.OA.2] Math Boxes: [ 4-3↔4-1]; 1 [2.OA.2]; 2 [2.MD.7]; 3 [2.NBT.2, 2.NBT.8]; 4 [2.MD.8]; 5 [2.NBT.4]; 6 [2.G.1] Part 3: Enrichment [2.G.1] Part 1: Focuses on solving problems where the unknown quantity is changing factor. [2.OA.1, 2.MD.6] Part 2: Math Boxes: [ 4-4↔4-2]; 1 [2.NBT.8]; 2, 4 [2.MD.8]; 3 [2.NBT.4]; 5 [2.OA.2]; 6 [2.G.1] Writing/Reasoning: [2.OA.1] SMP1, 2, 4–6; 2.OA.1 SMP1, 6; 2.OA.1, 2.NBT.5, 2.MD.6, 2.MD.8 SMP2–8; 2.OA.2, 2.MD.8, 2.G.1 SMP1, 2, 4–7; 2.OA.1, 2.MD.6 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 11 45 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.NBT.2]; Math Estimating Costs To guide children as they use estimation to solve problems for which an exact answer is not necessary. A Shopping Activity 46 To guide children as they develop strategies for adding multidigit numbers mentally; to provide experiences with calculating the total cost of two items; and to demonstrate making change for whole-dollar amounts up to $100. EXPLORATIONS: Exploring Length, Area, and Attributes 47 To guide children as they measure lengths and distances to the nearest inch and centimeter, explore area by tiling surfaces, and sort attribute blocks according to rules. Message [2.MD.8] Part 1: Focuses on using estimation as a strategy to add and subtract numbers. [2.MD.8] Part 2: Game: Name That Number [2.OA.2, 2.NBT.3] Math Boxes: [ 4-5↔4-7↔4-9]; 1 [2.MD.8]; 2 [Maintain]; 3 [2.OA.3]; 4 [2.MD.7]; 5 [2.NBT.5]; 6 [1.G.1] Home Link: [2.MD.8] Part 3: Readiness [2.MD.8] Getting Started: Mental Math and Reflexes [2.NBT.5, 2.NBT.6]; Math Message [2.OA.1, 2.NBT.9, 2.MD.8] Part 1: Focuses on strategies for adding and subtracting multidigit numbers. [2.OA.1, 2.NBT.5, 2.NBT.6, 2.NBT.9, 2.MD.6, 2.MD.8] Part 2: Game: Addition Spin [2.NBT.5] Math Boxes: [ 4-6↔4-8]; 1 [2.MD.8]; 2, 3 [2.OA.1]; 4 [2.MD.7]; 5 [2.MD.3]; 6 [2.G.1] Home Link: [2.OA.1, 2.NBT.5, 2.NBT.6] Part 3: Readiness and Extra Practice [2.NBT.5] Getting Started: Math Message [2.MD.1] Part 1: Provides practice measuring lengths, finding area by tiling, and sorting blocks according to their attributes. [2.MD.1, 2.MD.2, 2.G.2] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 4-7↔4-5↔4-9]; 1 [2.MD.8]; 2 [Maintain]; 3 [2.OA.3]; 4 [2.MD.7]; 5 [2.OA.2]; 6 [1.G.1] Home Link: [2.MD.1] Part 3: Enrichment [2.MD.1] SMP1, 3–7; 2.OA.2, 2.NBT.2, 2.MD.8 SMP1–7; 2.OA.1, 2.NBT.5, 2.NBT.6, 2.NBT.9, 2.MD.6, 2.MD.8 SMP1, 4–8; 2.OA.2, 2.MD.1, 2.MD.2, 2.G.2 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 12 48 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.NBT.5, 2.NBT.6] Paper-and-Pencil Addition Strategies To guide children as they develop paper-andpencil strategies for adding multidigit numbers; and to demonstrate using estimation to check if answers are reasonable. The Partial-Sums Addition Algorithm To introduce and practice the partial-sums addition algorithm. 49 Progress Check 4 410 To assess children’s progress on mathematical content through the end of Unit 4. Part 1: Focuses on developing strategies for adding multidigit numbers. [2.NBT.5. 2.NBT.6, 2.NBT.7, 2.NBT.9] Part 2: Game: Fact Extension Game [2.NBT.8] Math Boxes: [ 4-8↔4-6]; 1 [2.MD.8]; 2, 3 [2.OA.1]; 4 [2.MD.7]; 5 [2.MD.3]; 6 [2.G.1] Writing/Reasoning: [2.NBT.5, 2.NBT.9] Home Link: [2.NBT.5, 2.NBT.6, 2.NBT.7] Part 3: Readiness [2.NBT.8]; Enrichment [2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9] Getting Started: Mental Math and Reflexes [2.NBT.5, 2.NBT.7]; Home Link 4-8 Follow-Up [2.NBT.7, 2.NBT.9] Part 1: Focuses on practicing the partial-sums addition algorithm to solve addition problems. [2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9] Part 2: Game: Fact Extension Game [2.NBT.8] Math Boxes: [ 4-9↔4-5↔4-7]; 1 [2.MD.8]; 2 [Maintain]; 3 [2.OA.3]; 4 [2.MD.7]; 5 [2.OA.2]; 6 [1.G.1] Writing/Reasoning: [2.NBT.9] Home Link: [2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.6, 2.NBT.7] Part 3: Readiness [2.NBT.1]; Enrichment [2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9] Part 1: Checks children’s progress at the end of Unit 4. Part 2: Math Boxes: [ 4-10↔Unit 5]; 1, 4, 6 [2.G.1]; 2 [2.MD.1]; 3 [Maintain]; 5 [2.MD.3] SMP1, 3, 5–8; 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.8, 2.NBT.9 SMP1–3, 5–8; 2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9 * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 13 Unit 5 Copyright © The McGraw‐Hill Companies, Inc. 3‐D and 2‐D Shapes Weeks 12–14 (Lessons 51–59) CCSS Lesson Title/Objective EXPLORATIONS: Exploring Rules, Sharing, and Time 51 To demonstrate rules used to classify shapes; to develop readiness for division; and to demonstrate telling time using digital and analog notation. Points and Line Segments To guide children as they define, name, and draw line segments. 52 Focus Parallel Line Segments To introduce the concepts of parallel and parallel line segments. 53 Common Core State Standards* Getting Started: Mental Math and Reflexes [2.NBT.5]; Math Message [2.G.1] Part 1: Provides practice reading and writing time, dividing counters into groups, and grouping shapes based on attributes. [2.G.1, 2.MD.7] Part 2: Game: Addition Spin [2.NBT.5] Math Boxes: [ 5-1↔5-3]; 1 [2.NBT.5]; 2, 6 [2.MD.10]; 3 [2.NBT.7, 2.NBT.9]; 4 [Foundation]; 5 [2.G.1] Home Link: [2.G.1] Part 3: Readiness and Extra Practice [2.MD.7] Getting Started: Mental Math and Reflexes [2.OA.1] Part 1: Provides practice identifying the characteristics of points and line segments and drawing line segments using a straightedge. Defining and drawing line segments continues in Lesson 5-3. Part 2: Practicing with +, – Fact Triangles: [2.OA.2] Math Boxes: [ 5-2↔5-4]; 1 [2.NBT.2]; 2 [2.MD.10]; 3 [2.NBT.4]; 4 [2.OA.2]; 5 [2.MD.7]; 6 [2.OA.1] SMP2, 5–8; 2.NBT.5, 2.G.1, 2.MD.7 SMP1–2, 5, 6; 2.OA.1, 2.OA.2 Getting Started: Home Link Follow-Up [2.G.1] Part 1: Focuses on identifying the characteristics of parallel line segments. [2.G.1] Part 2: Solving Addition Problems Using Open Number Lines: [2.MD.6] Math Boxes: [ 5-3↔5-1]; 1 [2.NBT.3]; 2, 6 [2.MD.10]; 3 [2.NBT.7, 2.NBT.9]; 4 [Foundation]; 5 [2.G.1] Part 3: Enrichment [2.G.1] SMP1–6, 8; 2.MD.6, 2.G.1 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 14 54 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Math Message [2.G.1] EXPLORATIONS: Exploring Part 1: Focuses on building shapes that have specific Polygons, Arrays, and Attributes To review names and classify polygons; to develop readiness for multiplication; and to provide opportunities to explore similarities and differences of attribute blocks. Quadrangles 55 To guide children as they identify the names and characteristics of various quadrangles, and as they explore similarities and differences among quadrangles. 3-Dimensional Shapes To guide children as they compare and contrast the characteristics of 3-dimensional shapes. 56 Pyramids 57 To guide children as they construct pyramids and explore the relationship among the number of faces, edges, and vertices in pyramids. attributes, making arrays, and sorting attribute blocks. [2.OA.4, 2.G.1] Part 2: Game: Dollar Rummy [2.MD.8] Math Boxes: [ 5-4↔5-2]; 1 [2.NBT.2]; 2 [2.MD.10]; 3 [2.NBT.4]; 4 [2.OA.2]; 5 [2.MD.7]; 6 [2.OA.1] Home Link: [2.G.1] Part 3: Readiness, Enrichment, and Extra Practice [2.G.1] Getting Started: Math Message [2.G.1] Part 1: Focuses on identifying the attributes of quadrangles. [2.G.1] Part 2: Game: Name That Number [2.OA.2, 2.NBT.3] Math Boxes: [ 5-5↔5-7]; 1 [2.NBT.5]; 2 [Foundation]; 3, 4 [2.G.1]; 5 [2.NBT.4]; 6 [2.OA.2] Home Link: [2.OA.2, 2.G.1] Part 3: Readiness [2.G.1] Getting Started: Math Message [2.G.1]; Home Link Follow-Up [2.G.1] Part 1: Focuses on identifying the attributes of 3-dimensional shapes. [2.G.1] Part 2: Math Boxes: [ 5-6↔5-8]; 1 [2.NBT.2, 2.NBT.8]; 2, 5 [2.MD.8]; 3 [2.MD.10]; 4 [2.NBT.8]; 6 [Foundation] Home Link: [2.G.1] Part 3: Enrichment and Extra Practice [2.G.1] Getting Started: Mental Math and Reflexes [2.OA.2] Part 1: Focuses on identifying the attributes of pyramids. [2.G.1] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 5-7↔5-5]; 1 [2.NBT.5]; 2 [Foundation]; 3, 4 [2.G.1]; 5 [2.NBT.4]; 6 [2.OA.2] Home Link: [2.G.1] Part 3: Readiness, Enrichment, and ELL Support [2.G.1] SMP1, 2, 4–8; 2.OA.4, 2.G.1 SMP1, 2, 5–7; 2.OA.2, 2.G.1 SMP1–7; 2.G.1 SMP1, 2, 5–7; 2.OA.2, 2.G.1 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 15 58 Copyright © The McGraw‐Hill Companies, Inc. Line Symmetry To guide children as they find lines of symmetry in objects and complete drawings to create symmetrical shapes. Progress Check 5 59 To assess children’s progress on mathematical content through the end of Unit 5. Part 1: Introduces the concept of shapes’ lines of symmetry; provides practice identifying lines of symmetry, partitioning shapes based on lines of symmetry, and drawing symmetrical shapes. Partitioning shapes continues in Lesson 8-1. Part 2: Game: Fact Extension Game [2.NBT.8] Math Boxes: [ 5-8↔5-6]; 1 [2.NBT.2, 2.NBT.8]; 2, 5 [2.MD.8]; 3 [2.MD.10]; 4 [2.NBT.8]; 6 [2.MD.8] SMP1–6 Part 1: Checks children’s progress at the end of Unit 5. Part 2: Math Boxes: [ 5-9↔Unit 6]; 1, 5 [2.OA.4]; 2, 3 [2.MD.10]; 4 [Foundation]; 6 [2.OA.1] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 16 Unit 6 Copyright © The McGraw‐Hill Companies, Inc. Whole‐Number Operations and Number Stories Weeks 14–17 (Lessons 61–611) CCSS Lesson Title/Objective Focus Addition of Three or More Numbers To review strategies for solving addition problems, with emphasis on problems having three or more addends. 61 Comparison Number Stories To introduce comparison number stories by using comparison diagrams. 62 Common Core State Standards* Getting Started: Mental Math and Reflexes [2.NBT.5, 2.NBT.6]; Math Message [2.NBT.5] Part 1: Focuses on strategies for solving addition problems with three or more addends. [2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9, 2.MD.6] Part 2: Practicing Estimation and the Partial-Sums Algorithm [2.NBT.5, 2.NBT.7] Math Boxes: [ 6-1↔6-3↔6-5]; 1 [Foundation]; 2 [2.MD.3]; 3 [2.OA.1]; 4 [2.NBT.4]; 5 [2.OA.4]; 6 [2.NBT.2, 2.NBT.8] Home Link: [2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9] Part 3: Readiness [2.NBT.5, 2.NBT.9]; Enrichment [2.NBT.6, 2.NBT.9] Getting Started: Mental Math and Reflexes [2.NBT.6]; Math Message [2.OA.1, 2.MD.5]; Home Link Follow-Up [2.NBT.6] Part 1: Focuses on solving subtraction word problems. [2.MD.5] Part 2: Game: Addition Top-It [2.OA.2, 2.NBT.6] Math Boxes: [ 6-2↔6-4]; 1, 3 [2.NBT.5]; 2 [2.MD.8]; 4 [2.MD.3]; 5 [2.MD.7]; 6 [2.MD.8] Home Link: [2.OA.1, 2.NBT.6] Part 3: Enrichment [2.OA.1] SMP1–4, 6–8; 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.NBT.9, 2.MD.6 SMP1–6, 8; 2.OA.1, 2.NBT.6, 2.MD.5 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 17 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.MD.5] Data Day: The Five Food Groups To provide experiences with collecting, sorting, tallying, and graphing data. 63 Mixed Addition and Subtraction Stories 64 To guide children in selecting and completing appropriate diagrams to help solve one-and twostep addition and subtraction problems. Subtraction Strategies To review solution strategies for subtraction of multidigit numbers. 65 66 EXPLORATIONS: Exploring Arrays, Coins, and Division To develop readiness for multiplication; to guide children in finding coin combinations equivalent to $1.00; and to explore one meaning of division. Part 1: Focuses on collecting, representing, and interpreting data in a bar graph. [2.MD.10] Part 2: Comparing Lengths of Fish on the Fish Poster: [2.MD.5] Math Boxes: [ 6-3↔6-1↔6-5]; 1 [Foundation]; 2 [2.MD.3]; 3 [2.OA.1]; 4 [2.NBT.4]; 5 [Foundation]; 6 [2.NBT.2, 2.NBT.8] Writing/Reasoning: [2.MD.5] Home Link: [2.MD.10] Part 3: Readiness [2.MD.10] Getting Started: Mental Math and Reflexes [2.NBT.6]; Math Message [2.OA.1] Part 1: Focuses on solving number stories involving addition and subtraction. [2.OA.1] Part 2: Math Boxes: [ 6-4↔6-2]; 1 [2.NBT.8]; 2 [2.MD.8]; 3 [2.NBT.5]; 4 [2.MD.3]; 5 [2.MD.7]; 6 [2.MD.8] Home Link: [2.OA.1] Part 3: Readiness and Enrichment [2.OA.1] SMP1, 2, 4, 6; 2.MD.5, 2.MD.10 SMP1, 2, 4–6, 8; 2.OA.1, 2.NBT.6 Getting Started: Mental Math and Reflexes [2.NBT.5, 2.NBT.7]; Math Message [2.NBT.5, 2.NBT.9] Part 1: Focuses on reviewing strategies to solve subtraction problems. [2.NBT.2, 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.6] Part 2: Game: Number Grid Difference Game [2.NBT.5] Math Boxes: [ 6-5↔6-1↔6-3]; 1 [Foundation]; 2 [2.MD.3]; 3 [2.OA.1]; 4 [2.NBT.4]; 5 [Foundation]; 6 [2.NBT.2, 2.NBT.8] Home Link: [2.NBT.5, 2.NBT.7] Part 3: Readiness Playing the Base-10 Trading Game [2.NBT.7, 2.NBT.9]; Enrichment [2.NBT.5, 2.NBT.9] Getting Started: Math Message [2.OA.4] Part 1: Focuses on making arrays, working with coins, and equal sharing. [2.OA.4, 2.MD.8] Part 2: Making a Picture Graph: [2.MD.10] Math Boxes: [ 6-6↔6-8↔6-10]; 1 [2.NBT.5]; 2, 3 [Foundation]; 4 [2.OA.4]; 5 [Maintain]; 6 [Foundation] Home Link: [2.OA.4] Part 3: Enrichment and Extra Practice [2.MD.8] SMP1–6; 2.NBT.2, 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.6 SMP1, 2, 5–7; 2.OA.4, 2.MD.8, 2.MD.10 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 18 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.MD.5]; Math Multiples of Equal Groups To introduce multiplication as a way to find the total number of things in several equal groups. 67 Array Number Stories 68 69 To introduce everyday examples of rectangular arrays; and to provide experiences with solving multiplication problems using multiplication diagrams and array models. Multiplication with Arrays To introduce everyday examples of arrays; and to provide experiences with solving multiplication problems using multiplication diagrams and array models. Division Stories 610 To guide children as they explore situations that require equal sharing or making equal groups of things. Message [2.OA.4] Part 1: Focuses on solving problems involving equal groups of objects. [2.OA.4] Part 2: Practicing with +/– Fact Triangles: [2.OA.2] Math Boxes: [ 6-7↔6-9]; 1 [2.NBT.7, 2.NBT.9]; 2 [Foundation]; 3 [2.MD.1]; 4 [2.NBT.5]; 5 [Maintain]; 6 [2.OA.2] Home Link: [2.OA.4] Part 3: Readiness and Enrichment [2.OA.4] Getting Started: Math Message [2.OA.4] Part 1: Focuses on using strategies to solve problems involving rectangular arrays. [2.OA.4] Part 2: Game: Fact Extension Game [2.NBT.8] Math Boxes: [ 6-8↔6-6↔6-10]; 1 [2.NBT.5]; 2, 3 [Foundation]; 4 [2.OA.4]; 5 [2.NBT.5]; 6 [Foundation] Home Link: [2.OA.4] SMP1–6; 2.OA.2, 2.OA.4, 2.MD.5 SMP1, 2, 4–6; 2.OA.4 Getting Started: Math Message [2.OA.4]; Home Link Follow-Up [2.OA.4] Part 1: Focuses on strategies to find the total number of objects in a rectangular array. [2.OA.4] Part 2: Game: Array Bingo [2.OA.4] Math Boxes: [ 6-9↔6-7]; 1, 4 [2.NBT.7, 2.NBT.9]; 2 [Foundation]; 3 [2.MD.1]; 5 [Maintain]; 6 [2.OA.2] Home Link: [2.OA.4] Part 3: Readiness [2.OA.4] Part 1: Begins developing the concept of division through equal-sharing and equal-grouping situations. Division is addressed again in Lesson 11-5. Part 2: Game: Number-Grid Difference Game [2.NBT.5] Math Boxes: [ 6-10↔6-6↔6-8]; 1 [2.NBT.3]; 2, 3 [Foundation]; 4 [2.OA.4]; 5 [2.NBT.5]; 6 [Foundation] SMP1, 2, 4–7; 2.OA.4 SMP1, 2, 4–6, 8 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 19 611 Copyright © The McGraw‐Hill Companies, Inc. Part 1: Checks children’s progress at the end of Unit 6. Progress Check 6 To assess children’s progress on mathematical content through the end of Unit 6. Part 2: Math Boxes: [ 6-11↔Unit 7]; 1 [2.OA.2]; 2 [2.MD.10]; 3 [2.MD.8]; 4 [2.MD.8]; 5 [Foundation]; 6 [2.G.3] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 20 Unit 7 Copyright © The McGraw‐Hill Companies, Inc. Patterns and Rules Weeks 17–19 (Lessons 71–79) CCSS Lesson Title/Objective Patterns in Counting 71 To review counting by 2s, 5s, and 10s; to extend this to counting by any number n; and to provide experiences with describing patterns that result from counting. Focus Extending Complements of 10 72 To provide experiences with finding complements of 10 and differences between multidigit numbers and higher multiples of 10. Mental Arithmetic: A Basketball Game 73 To guide children as they build mental arithmetic skills for adding three or more 1-digit and multidigit numbers. Common Core State Standards* Getting Started: Math Message [2.NBT.2] Part 1: Focuses on skip-counting and describing the patterns that develop. [2.NBT.2] Part 2: Math Boxes: [ 7-1↔7-3]; 1 [Foundation]; 2 [2.NBT.5]; 3 [2.OA.4]; 4 [2.MD.8]; 5 [Foundation]; 6 [2.G.3] Home Link: [2.NBT.2] Part 3: Readiness, Enrichment, Extra Practice, and ELL Support [2.NBT.2] Getting Started: Math Message [2.NBT.5] Part 1: Focuses on using a calculator to practice skip counting by 10 and introduces the game Hit the Target. [2.NBT.5] Part 2: Solving Subtraction Problems: [2.NBT.7] Math Boxes: [ 7-2↔7-4]; 1 [2.OA.4]; 2 [2.NBT.6]; 3 [Foundation]; 4 [Foundation]; 5 [2.NBT.7]; 6 [2.G.3] Home Link: [2.NBT.5, 2.NBT.7] Part 3: Readiness and Extra Practice [2.NBT.5] Getting Started: Math Message [2.NBT.6] Part 1: Introduces the game Basketball Addition to practice solving addition problems. [2.NBT.6, 2.MD.6] Part 2: Math Boxes: [ 7-3↔7-1]; 1 [Foundation]; 2 [2.NBT.5]; 3 [2.OA.4]; 4 [2.NBT.3]; 5 [Foundation]; 6 [2.G.3] Home Link: [2.NBT.6] Part 3: Readiness [2.NBT.6] SMP5–7; 2.NBT.2 SMP1, 3, 5–8; 2.NBT.5, 2.NBT.7 SMP1, 2, 4–8; 2.NBT.6, 2.MD.6 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 21 74 75 Copyright © The McGraw‐Hill Companies, Inc. Part 1: Provides practice with repeated doubling and halving Patterns in Doubles and Halves To guide children as they practice repeated doubling and halving. EXPLORATIONS: Exploring Weights, Equal Sharing, and Patterns To provide experiences with exploring weights in pounds on a bath scale, developing readiness for division, and exploring area and patterns. Data Day: Standing Jumps and Arm Spans 76 77 To guide children as they measure length to the dearest centimeter and to the nearest inch. Middle Value (Median) of a Set of Data To guide children as they sort numerical data and arrange data in ascending or descending order, and as they find the middle value (median) for a set of numerical data. and with developing strategies for multiplying and dividing by 2. Work with multiplication and division continues in Lessons 11-4 through 11-9. Part 2: Game: Hit the Target [2.NBT.5] Math Boxes: [ 7-4↔7-2]; 1 [2.OA.4]; 2 [2.NBT.6]; 3 [Foundation]; 4 [Foundation]; 5 [2.OA.2]; 6 [2.G.3] SMP1, 2, 5–8 Getting Started: Mental Math and Reflexes [2.MD.8] Part 1: Focuses on exploring weights, solving problems involving sharing money, and making patterns related to area. [2.MD.8] Part 2: Game: Hit the Target [2.NBT.5] Math Boxes: [ 7-5↔7-7]; 1 [2.MD.7]; 2 [2.MD.10]; 3 [2.OA.4]; 4 [Foundation]; 5 [2.G.1]; 6 [2.G.3] Part 3: Readiness [2.MD.8] Getting Started: Math Message [2.MD.2] Part 1: Focuses on measuring length and recording the data. [2.MD.1, 2.MD.2, 2.MD.4, 2.MD.9] Part 2: Game: Array Bingo [2.OA.4] Math Boxes: [ 7-6↔7-8]; 1 [2.MD.8]; 2 [Foundation]; 3 [Maintain]; 4 [2.NBT.3]; 5 [Foundation]; 6 [2.G.3] Home Link: [2.MD.1, 2.MD.4] SMP1–8; 2.MD.8 SMP2, 3, 5, 6; 2.MD.1, 2.MD.2, 2.MD.4, 2.MD.9 Getting Started: Mental Math and Reflexes [2.NBT.4] Part 1: Focuses on sorting data and finding the median. [2.MD.5] Part 2: Measuring Objects: [2.MD.4, 2.MD.5] Math Boxes: [ 7-7↔7-5]; 1 [2.MD.7]; 2 [2.MD.10]; 3 [2.OA.4]; 4 [Foundation]; 5 [2.G.1]; 6 [2.G.3] Home Link: [2.NBT.4] Part 3: Readiness [2.NBT.4] SMP1–7; 2.NBT.4, 2.MD.4, 2.MD.5 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 22 78 Copyright © The McGraw‐Hill Companies, Inc. Part 1: Focuses on organizing and interpreting data in a line Frequency Distributions To guide children as they make a frequency table, line plot, and bar graph for a set of data; and as they find the median of a set of data. Progress Check 7 79 To assess children’s progress on mathematical content through the end of Unit 7. plot and bar graph. [2.MD.4, 2.MD.5, 2.MD.9, 2.MD.10] Part 2: Game: Soccer Spin [Foundation] Math Boxes: [ 7-8↔7-6]; 1 [2.MD.8]; 2 [Foundation]; 3 [Maintain]; 4 [2.NBT.3]; 5 [Foundation]; 6 [2.G.3] Part 3: Enrichment [2.MD.10] Part 1: Checks children’s progress at the end of Unit 7. Part 2: Math Boxes: [ 7-9↔Unit 8]; 1, 2, 4, 6 [2.G.3]; 3 [2.NBT.7, 2.NBT.9]; 5 [Foundation] SMP1, 2, 4, 6; 2.MD.4, 2.MD.5, 2.MD.9, 2.MD.10 * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 23 Unit 8 Copyright © The McGraw‐Hill Companies, Inc. Fractions Weeks 19–21 (Lessons 81–88) CCSS Lesson Title/Objective Equal Parts of ONE To review basic fraction concepts. 81 EXPLORATIONS: Exploring Fractions, Multiplication and Division, and Volume 82 To guide children as they explore the link of a fraction amount to the size of the ONE, or whole; to prepare for multiplication and division; and to introduce the concept of volume. Collections of Things 83 84 Focus To guide children as they use fractions to name parts of collections. Equivalent Fractions To provide experiences with the idea that many different fractions can name the same fractional part of a whole. Common Core State Standards* Getting Started: Mental Math and Reflexes [2.OA.2]; Math Message [2.G.3] Part 1: Focuses on dividing shapes into equal parts and writing fractions. [2.G.3] Part 2: Bamboo Plant Number Stories: [2.MD.5] Math Boxes: [ 8-1↔8-3]; 1, 3, 5, 6 [Foundation]; 2 [2.G.1]; 4 [2.MD.8] Home Link: [2.G.3] Part 3: Enrichment and Extra Practice [2G.3] Part 1: Provides practice describing shares of objects, making arrays, and finding volumes. [2.G.3] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 8-2↔8-4↔8-6]; 1, 4 [Foundation]; 2 [Maintain]; 3 [2.NBT.1b]; 5 [2.MD.1]; 6 [2.G.2] Home Link: [2.G.3] Part 3: Enrichment [2.G.3] SMP1–4, 6; 2.OA.2, 2.MD.5, 2.G.3 SMP2, 4–6; 2.OA.2, 2.G.3 Getting Started: Home Link Follow-Up [2.G.3] Part 1: Provides practice describing shares of collections. Part 2: Counting Equal Parts: [2.G.3] Math Boxes: [ 8-3↔8-1]; 1 [2.G.3]; 2 [2.G.1]; 3, 5, 6 [Foundation]; 4 [2.MD.8] SMP1, 2, 4–6; 2.G.3 Part 1: Introduces the concept that different fractions can describe equal amounts in preparation for Lesson 8-5. [2.G.3] Part 2: Game: Name That Number [2.NBT.3] Math Boxes: [ 8-4↔8-2↔8-6]; 1 [Foundation]; 2 [Maintain]; 3 [2.NBT.5]; 4 [2.G.3]; 5 [2.MD.1]; 6 [2.G.2] Home Link: [2.G.3] Part 3: Readiness [2.G.3] SMP1, 2, 5–7; 2.G.3 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 24 Copyright © The McGraw‐Hill Companies, Inc. Part 1: Introduces Fraction Cards and the Equivalent Fractions Equivalent Fractions Using Fraction Game. [2.G.3] Cards 85 To guide children as they find pairs of equivalent fractions by using region models. Comparing Fractions 86 87 88 To guide children as they compare fractions by using region models. Fraction Number Stories To provide experiences with number stories involving fractions. Progress Check 8 To assess children’s progress on mathematical content through the end of Unit 8. SMP1–7; Part 2: Math Boxes: [ 8-5↔8-7]; 1 [2.MD.10]; 2 [Foundation]; 3 [2.NBT.7]; 4 [2.NBT.5]; 5, 6 [2.MD.1] Home Link: [2.G.3] Part 3: Enrichment [2.G.3] Part 1: Focuses on comparing fractions. [2.G.3] Part 2: Game: Equivalent Fractions Game [Foundation] Math Boxes: [ 8-6↔8-2↔8-4]; 1, 4 [Foundation]; 2 [Maintain]; 3 [2.NBT.1b]; 5 [2.MD.1]; 6 [2.G.2] 2.G.3 SMP1, 2, 5–8; 2.G.3 Part 1: Focuses on solving word problems involving fractions. [2.G.3] Part 2: Game: Fraction Top-It [Foundation] Math Boxes: [ 8-7↔8-5]; 1 [2.MD.10]; 2 [Foundation]; 3, 4 [2.NBT.5]; 5, 6 [2.MD.1] SMP1, 2, 4–6; 2.G.3 Part 1: Checks children’s progress at the end of Unit 8. Part 2: Math Boxes: [ 8-8↔Unit 9]; 1, 5 [Foundation]; 2, 4 [2.MD.1]; 3, 6 [2.G.2] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 25 Unit 9 Copyright © The McGraw‐Hill Companies, Inc. Measurement Weeks 21–24 (Lessons 91–910) CCSS Lesson 91 Title/Objective Measuring with Yards and Meters To provide review for the concept of nonstandard units of measure; and to introduce yard and meter. Linear Measures 92 To provide review for measuring with inches, feet, centimeters, and decimeters; and to guide children as they begin a table of equivalent linear measures. Fractional Units of Length 93 Focus To guide children as they investigate the idea of accuracy, explore 1/8 inch, 1/16 inch, and 1/2 centimeter on a ruler, and explore measuring to the nearest half-inch and half-centimeter. Common Core State Standards* Part 1: Focuses on measuring length with yardsticks and metersticks to whole units. [2.MD.1, 2.MD.3] Part 2: Comparing Measurements: [2.MD.4, 2.MD.9] Math Boxes: [ 9-1↔9-3]; 1 [2.OA.4]; 2 [2.NBT.5]; 3 [Foundation]; 4 [2.NBT.3]; 5 [2.MD.3]; 6 [2.MD.8] Home Link: [2.MD.1] Part 3: Enrichment [2.MD.3, 2.MD.4] Getting Started: Mental Math and Reflexes [2.OA.2] Part 1: Focuses on measuring lengths of objects to whole units. [2.MD.1, 2.MD.2, 2.MD.3] Part 2: Game: Name That Number [2.NBT.3] Math Boxes: [ 9-2↔9-4]; 1, 4, 5 [Foundation]; 2 [2.MD.1]; 3 [2.OA.1]; 6 [2.MD.8] Home Link: [2.MD.1, 2.MD.2] Part 3: Extra Practice [2.MD.4] Getting Started: Math Message [2.MD.1, 2.MD.3] Part 1: Focuses on measuring lengths of objects to fractions of the unit. [2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4] Part 2: Practicing with +, – Fact Triangles: [2.OA.2] Math Boxes: [ 9-3↔9-1]; 1 [2.OA.4]; 2 [2.NBT.4]; 3 [2.MD.1]; 4 [2.NBT.3]; 5 [2.MD.3]; 6 [2.MD.8] Home Link: [2.MD.1] Part 3: Readiness [2.MD.3]; Enrichment [2.MD.1, 2.MD.2] SMP1, 2, 4–6; 2.MD.1, 2.MD.3, 2.MD.4, 2.MD.9 SMP1, 2, 5–7; 2.OA.2, 2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4 SMP2–6; 2.OA.2, 2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 26 Copyright © The McGraw‐Hill Companies, Inc. Perimeter 94 95 To provide experiences with finding perimeters by measuring to the nearest centimeter or inch. 97 To provide experiences with identifying the mile and kilometer as standard units for longer distances and solving problems about road-map distances. To guide children as they explore the capacities of cylinders, find the areas of shapes by using inch and centimeter grids, and explore measuring tools and units of measure. Area To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. Capacity 98 Measuring Longer Distances EXPLORATIONS: Exploring Capacity, Area, and Measures 96 To provide experiences with relationships among units of capacity and identifying equivalent measures of capacity. Getting Started: Math Message [2.MD.1] Part 1: Focuses on measuring the length to find the perimeter of an object. [2.MD.1, 2.MD.9] Part 2: Game: Number Grid Difference Game [2.NBT.5] Math Boxes: [ 9-4↔9-2]; 1, 4, 5 [Foundation]; 2 [2.MD.1]; 3 [2.OA.1]; 6 [2.MD.8] Home Link: [2.MD.1] SMP1, 3–6; 2.MD.1, 2.MD.9 Part 1: Focuses on using addition strategies to calculate total distance. [2.NBT.7] Part 2: Practicing 2-Digit Addition and Subtraction: [2.NBT.5] Math Boxes: [ 9-5↔9-7↔9-9]; 1 [2.G.3]; 2 [2.OA.3]; 3 [Foundation]; 4 [Foundation]; 5, 6 [2.NBT.5] Writing/Reasoning: [2.NBT.5] Part 3: Enrichment [2.NBT.7] Part 1: Focuses on the characteristics of cylinders, finding areas of shapes by counting squares, and exploring measuring tools. [2.G.2] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 9-6↔9-8]; 1 [2.NBT.4]; 2 [2.NBT.5]; 3 [2.NBT.5]; 4 [2.MD.1]; 5 [Foundation]; 6 [2.MD.8] Home Link: [2.G.2] SMP2, 4–7; 2.NBT.5, 2.NBT.7 SMP1, 2, 4–6, 8; 2.OA.2, 2.G.2 Part 1: Focuses on finding area by partitioning and counting the equal parts. [2.G.2] Part 2: Game: Equivalent Fractions Game or Fraction Top-It [Foundation] Math Boxes: [ 9-7↔9-5↔9-9]; 1, 3 [Foundation]; 2 [2.OA.3]; 4 [Foundation]; 5, 6 [2.NBT.5] Home Link: [2.G.2] Part 3: Readiness and Extra Practice [2.G.2] Part 1: Focuses on U.S. customary units of capacity. Part 2: Reviewing Line Plot Routine: [2.MD.9] Math Boxes: [ 9-8↔9-6]; 1 [2.NBT.4]; 2 [2.NBT.5]; 3 [2.NBT.5]; 4 [2.MD.1]; 5 [Foundation]; 6 [2.MD.8] SMP1–3, 5, 6; 2.G.2 SMP1, 2, 4–6, 8; 2.MD.9 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 27 Copyright © The McGraw‐Hill Companies, Inc. Weight 99 To guide children as they compare weights by feel, identify purposes of various scales, explore with units of weight and equivalent measures, and weigh objects. Progress Check 9 910 To assess children’s progress on mathematical content through the end of Unit 9. Part 1: Focuses on U.S. customary units of weight. Part 2: Game: Name That Number [2.OA.2, 2.NBT.3] Math Boxes: [ 9-9↔9-5↔9-7]; 1 [2.G.3]; 2 [2.OA.3]; 3 [Foundation]; 4 [2.MD.8]; 5, 6 [2.NBT.5] SMP1, 4–6, 8; 2.OA.2 Part 1: Checks children’s progress at the end of Unit 9. Part 2: Math Boxes: [ 9-10↔Unit 10]; 1, 3, 4, 5, 6 [2.MD.8]; 2 [2.NBT.5] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 28 Unit 10 Copyright © The McGraw‐Hill Companies, Inc. Decimals and Place Value Weeks 24–27 (Lessons 101–1012) CCSS Lesson Title/Objective Money To review notation and equivalencies for money amounts. 101 Decimal Notation for Pennies and Dimes 102 To review estimation, dollars-and-cents notation, and names for a dollar, a dime, and a penny. Money Amounts with a Calculator To guide children as they enter money amounts into a calculator and interpret calculator displays. Focus 103 Common Core State Standards* Getting Started: Math Message [2.MD.8] Part 1: Focuses on written notation for money and equivalent money amounts. [2.MD.8] Part 2: Game: Spinning for Money [2.MD.8] Math Boxes: [ 10-1↔10-3↔10-5]; 1 [2.NBT.2, 2.NBT.8]; 2, 3 [Foundation]; 4 [2.NBT.8]; 5 [2.G.1]; 6 [2.OA.4] Home Link: [2.MD.8] Part 3: Readiness, Enrichment, and Enrichment [2.MD.8] Part 1: Provides practice writing decimal notation for money amounts and representing the values of coins using different names. Using decimal notation for money amounts continues in Lesson 10-4. Part 2: Math Boxes: [ 10-2↔10-4]; 1 [2.NBT.4]; 2, 6 [Foundation]; 3 [2.NBT.3]; 5 [2.MD.7] SMP1, 2, 4, 6, 7; 2.MD.8 SMP1–4, 6 Getting Started: Mental Math and Reflexes [2.MD.8] Part 1: Focuses on how to display money amounts on a calculator and introduces the game Pick-a-Coin. [2.MD.8] Part 2: Using Square Units to Find Area: [2.G.2] Math Boxes: [ 10-3↔10-1↔10-5]; 1 [2.MD.8]; 2 [Foundation]; 3 [2.NBT.8]; 4 [2.NBT.8]; 5 [Maintain]; 6 [2.OA.4] Writing/Reasoning: [2.MD.8] Home Link: [2.MD.8] Part 3: Enrichment [2.OA.1, 2.MD.8] SMP1, 2, 5–8; 2.OA.1, 2.MD.8, 2.G.2 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 29 104 Copyright © The McGraw‐Hill Companies, Inc. Using a Calculator to Solve Problems Getting Started: Mental Math and Reflexes [2.MD.8] Part 1: Focuses on solving problems involving money on a with Money To provide experiences with comparing prices and solving problems about price differences. Estimating and Finding Exact Costs To provide experiences with estimating costs and then calculating exact costs. Making Change To provide experience making change by counting up and estimating totals by rounding to the nearest 10 cents. EXPLORATIONS: Exploring Area, Polygons, and Geoboard Fractions 107 105 106 To guide children as they explore finding areas of irregular shapes, make polygons with trapezoids, and form fractions on a geoboard. calculator. [2.OA.1, 2.MD.8] Part 2: Game: Pick-a-Coin [2.MD.8] Math Boxes: [ 10-4↔10-2]; 1 [2.NBT.4]; 2, 6 [Foundation]; 3 [2.NBT.3]; 5 [2.MD.7] Home Link: [2.MD.8] Part 3: Readiness and Enrichment [2.OA.1, 2.MD.8] Getting Started: Mental Math and Reflexes [2.MD.8]; Math Message [2.MD.8] Part 1: Focuses on estimating costs to quickly calculate an approximate value. [2.MD.8] Part 2: Displaying Shoe Length Data on a Line Plot: [2.MD.9] Math Boxes: [ 10-5↔10-1↔10-3]; 1, 2 [2.MD.8]; 3 [Foundation]; 4 [2.NBT.8]; 5 [Maintain]; 6 [2.OA.4] Home Link: [2.MD.8] SMP1, 3–7; 2.OA.1, 2.MD.8 SMP1–7; 2.MD.8, 2.MD.9 Getting Started: Mental Math and Reflexes [2.MD.8] Part 1: Provides practice using the subtraction strategy of counting up. [2.OA.1, 2.MD.8] Part 2: Game: Equivalent Fractions or Fraction Top-It [Foundation] Math Boxes: [ 10-6↔10-8↔10-10]; 1 [2.NBT.5]; 2, 4 [2.MD.8]; 3 [Maintain]; 5 [2.G.1]; 6 [Foundation] Writing/Reasoning: [2.OA.1] Home Link: [2.MD.8] Part 3: Readiness [2.OA.1]; Enrichment [2.MD.8] Part 1: Provides practice estimating area of irregular shapes, making polygons, and partitioning shapes into equal parts. [2.G.3] Part 2: Game: Beat the Calculator [2.OA.2] Math Boxes: [ 10-7↔10-9↔10-11]; 1 [2.G.3]; 2, 3 [2.MD.8]; 4 [2.NBT.5]; 5 [Maintain]; 6 [Foundation] Part 3: Readiness and Enrichment [2.G.3] SMP1, 3–7; 2.OA.1, 2.MD.8 SMP1, 2, 5–8; 2.OA.2, 2.G.3 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 30 Copyright © The McGraw‐Hill Companies, Inc. Place Value 108 To develop place-value concepts and connect place value in money with place value in base-10 blocks. Place-Value Tools To develop place-value concepts by using placevalue tools. 109 1010 Place-Value Notation for TenThousands To provide experiences with place-value concepts to ten-thousands. Grouping with Parentheses 1011 To introduce the use of parentheses in number models. Progress Check 10 1012 To assess children’s progress on mathematical content through the end of Unit 10. Getting Started: Math Message [2.NBT.1, 2.NBT.1a] Part 1: Focuses on understanding place value. [2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.8] Part 2: Math Boxes: [ 10-8↔10-6↔10-10]; 1 [2.NBT.5]; 2, 4 [2.MD.8]; 3 [2.OA.1]; 5 [2.G.1]; 6 [Foundation] Home Link: [2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.3] Part 3: Readiness [2.NBT.1, 2.NBT.1b]; Extra Practice [2.NBT.4] Getting Started: Math Message [2.NBT.1, 2.NBT.1b. 2.NBT.3] Part 1: Focuses on making and using the Place-Value tool. [2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.8] Part 2: Practicing Routines with Place Value Tools: [2.NBT.1, 1.NBT.1a, 2.NBT.1b, 2.NBT.3] Math Boxes: [ 10-9↔10-7↔10-11]; 1, 6 [Foundation]; 2 [2.G.3]; 3 [2.MD.8]; 4 [2.NBT.5]; 5 [Maintain] Home Link: [2.NBT.8] Part 3: Readiness [2.NBT.1, 2.NBt.1a, 2.NBT.1b, 2.NBT.3]; Extra Practice [2.NBT.1] Getting Started: Mental Math and Reflexes [2.NBT.1, 2.NBT.1b] Part 1: Focuses on extending understanding of place value to the ten-thousands place. [2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.8] Part 2: Math Boxes: [ 10-10↔10-6↔10-8]; 1 [2.NBT.5]; 2, 4 [2.MD.8]; 3 [Maintain]; 5 [2.G.1]; 6 [Foundation] Home Link: [2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.3, 2.NBT.8] Part 3: Enrichment [2.NBT.4] Getting Started: Mental Math and Reflexes [2.NBT.3] Part 1: Focuses on the using parentheses in number models. [2.NBT.6] Part 2: Game: Soccer Spin [Foundation] Math Boxes: [ 10-11↔10-7↔10-9]; 1, 6 [Foundation]; 2 [2.G.3]; 3 [2.MD.8]; 4 [2.MD.8]; 5 [Maintain] SMP1, 2, 5–7; 2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.4, 2.NBT.8 SMP1, 2, 5–8; 2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.8 SMP1, 2, 5–7; 2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.4, 2.NBT.8 SMP1, 2, 5–8; 2.NBT.3, 2.NBT.6 Part 1: Checks children’s progress at the end of Unit 10. Part 2: Math Boxes: [ 10-12↔Unit 11]; 1, 3, 4, 6 [Foundation]; 2, 5 [2.OA.4] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 31 Unit 11 Copyright © The McGraw‐Hill Companies, Inc. Whole‐Number Operations Revisited Weeks 27–29 (Lessons 111–1110) CCSS Lesson 111 Title/Objective Addition Number Stories with Dollars and Cents To guide children as they review finding estimates for sums of money, and calculate values of coin and bill combinations in number stories. Subtraction Number Stories with Dollars and Cents 112 113 Focus To guide children as they review making change by counting up, and solve comparison number stories with money. The Trade-First Subtraction Algorithm To introduce and provide practice with the tradefirst subtraction algorithm. Common Core State Standards* Getting Started: Math Message [2.MD.8] Part 1: Provides practice solving addition word problems involving money. [2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.6, 2.MD.8] Part 2: Game: Hit the Target [2.NBT.5] Math Boxes: [ 11-1↔11-3]; 1 [2.MD.3]; 2, 6 [Foundation]; 3 [2.NBT.5]; 4 [2.OA.4]; 5 [2.MD.8] Writing/Reasoning: [2.MD.8] Home Link: [2.MD.8] Part 3: Readiness [2.MD.8] Getting Started: Math Message [2.MD.8]; Home Link Follow-Up [2.MD.8] Part 1: Provides practice solving subtraction word problems involving money. [2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.8] Part 2: Math Boxes: [ 11-2↔11-4]; 1 [2.NBT.5]; 2 [2.NBT.3]; 3 [2.G.1]; 4 [Foundation]; 5 [Foundation]; 6 [2.NBT.7] Home Link: [2.MD.8] Part 3: Readiness [2.NBT.5, 2.NBT.7]; Enrichment [2.MD.8] Getting Started: Mental Math and Reflexes [2.NBT.5] Part 1: Introduces the trade-first subtraction algorithm as a strategy for solving problems with multidigit numbers. [2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.7, 2.NBT.9] Part 2: Displaying Head Size Data on a Line Plot: [2.MD.9] Math Boxes: [ 11-3↔11-1]; 1 [2.MD.3]; 2 [2.G.3]; 3 [2.NBT.5]; 4 [2.OA.4]; 5 [2.MD.8]; 6 [Foundation] Home Link: [2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.7] Part 3: Readiness [2.NBT.1, 2.NBT.1a]; Enrichment [2.NBT.5, 2.NBT.7] SMP1, 4–7; 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.6, 2.MD.8 SMP1, 2, 4–7; 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.8 SMP1–7; 2.NBT.1, 2.NBT.1a, 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.9 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 32 114 115 Copyright © The McGraw‐Hill Companies, Inc. Part 1: Focuses on solving number stories involving equal Multiples of Equal Groups To provide experiences with finding the total number of items in several equal groups by multiplying. Division Number Models To provide experiences with solving division number stories; and to introduce number models for division stories. Multiplication Facts 116 To introduce multiplication facts; and to provide review and practice with multiplying by 2, 5, and 10. 118 Products Table 117 To introduce 1s and 0s multiplication facts; and to guide children as they discover patterns in multiplication facts. Multiplication/Division Fact Families To introduce multiplication and division fact families; and to provide practice with multiplication and division facts. groups of objects. [2.OA.4] Part 2: Game: Array Bingo [2.OA.4] Math Boxes: [ 11-4↔11-2]; 1 [2.NBT.5]; 2 [2.NBT.3]; 3 [2.G.1]; 4 [Foundation]; 5 [Foundation]; 6 [2.NBT.7] SMP1, 2, 4–6; 2.OA.4 Part 1: Provides practice using equal groups and equal shares to model division and writing number sentences to model number stories. Work with division continues in Lessons 11-8 and 11-9. Part 2: Game: Soccer Spin [Foundation] Math Boxes: [ 11-5↔11-7↔11-9]; 1 [2.NBT.2, 2.NBT.8]; 2 [2.OA.4]; 3 [2.NBT.5]; 4 [2.NBT.2]; 5 [2.MD.1]; 6 [Foundation] SMP1, 2, 4–6 Getting Started: Math Message [2.OA.4] Part 1: Focuses on multiplication and its relation to arrays and skip counting. [2.OA.4] Part 2: Game: Name That Number [2.NBT.3] Math Boxes: [ 11-6↔11-8]; 1 [2.NBT.5]; 2, 6 [2.NBT.3]; 3 [2.MD.1]; 4 [2.G.3]; 5 [2.NBT.5] Part 3: Enrichment [2.OA.4] Part 1: Focuses on the completing a Products Table and finding patterns in it. [2.OA.4] Part 2: Math Boxes: [ 11-7↔11-5↔11-9]; 1 [2.NBT.2, 2.NBT.8]; 2 [2.OA.4]; 3 [2.NBT.5]; 4 [2.NBT.2]; 5 [2.MD.1]; 6 [Foundation] SMP1, 2, 5–7; 2.OA.4 SMP1, 2, 4, 6–8; 2.OA.4 Part 1: Introduces multiplication and division fact families, focusing on the relationship between multiplication and division. Practice with multiplication and division facts continues in Lesson 11-9. Part 2: Math Boxes: [ 11-8↔11-6]; 1 [2.NBT.5]; 2, 6 [2.NBT.3]; 3 [2.MD.1]; 4 [2.G.3]; 5 [2.NBT.8] SMP1–4, 7, 8 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 33 119 Copyright © The McGraw‐Hill Companies, Inc. Multiplication/Division Facts Practice Part 1: Provides practice with multiplication and division facts. To provide practice with multiplication and division facts. Progress Check 11 1110 To assess children’s progress on mathematical content through the end of Unit 11. Work with multiplication and division continues in Lessons 124 and 12-5. Part 2: Math Boxes: [ 11-9↔11-5↔11-7]; 1 [2.NBT.2, 2.NBT.8]; 2 [Foundation]; 3 [2.NBT.5]; 4, 6 [2.NBT.2]; 5 [2.MD.1] SMP1–6 Part 1: Checks children’s progress at the end of Unit 11. Part 2: Math Boxes: [ 11-10↔Unit 12]; 1, 2, 4 [2.NBT.3]; 3, 5, 6 [Foundation] * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 34 Unit 12 Copyright © The McGraw‐Hill Companies, Inc. Year‐End Reviews and Extensions Weeks 29–31 (Lessons 121–128) CCSS Lesson 121 122 Title/Objective Review: The Calendar To guide children as they review time equivalencies and calendar facts. Review: Clock Skills To guide children as they review reading times in different ways, show time to the nearest five minutes on a clock face, and calculate times relative to a given time. Timelines 123 To provide experiences with events on a timeline. Practice Multiplication Facts 124 Focus To provide review and extend shortcuts and strategies for learning multiplication facts; and to provide practice for multiplication facts. Common Core State Standards* Part 1: Focuses on reviewing time equivalencies and practicing reading and writing time. [2.MD.7] Part 2: Math Boxes: [ 12-1↔12-3]; 1, 4 [2.MD.8]; 2 [Maintain]; 3 [2.G.3]; 5 [2.NBT.3]; 6 [2.G.1] Part 3: Readiness [2.MD.7] Getting Started: Math Message [2.MD.7] Part 1: Focuses on reviewing reading and writing time on digital and analog clock. [2.MD.7] Part 2: Game: Beat the Calculator [2.OA.2] Solving Multidigit Addition and Subtraction Problems: [2.NBT.5, 2.NBT.7] Math Boxes: [ 12-2↔12-4↔12-6]; 1 [2.MD.10]; 2 [2.NBT.5]; 3 [2.NBT.4]; 4 [2.G.1]; 5 [2.G.2]; 6 [Foundation] Home Link: [2.MD.7] Part 3: Extra Practice [2.MD.7] Part 1: Focuses on ordering dates on a number line. [2.MD.6] Part 2: Math Boxes: [ 12-3↔12-1]; 1, 4 [2.MD.8]; 2 [Maintain]; 3 [2.G.3]; 5 [2.NBT.3]; 6 [2.G.1] Part 3: Readiness [2.MD.6]; Enrichment [2.MD.6] Part 1: Focuses on practicing multiplication facts. Part 2: Game: Name That Number [2.NBT.3] Practicing Estimation and the Trade-First Algorithm: [2.NBT.5, 2.NBT.7] Math Boxes: [ 12-4↔12-2↔12-6]; 1 [2.MD.10]; 2 [2.NBT.5]; 3 [2.NBT.4]; 4 [2.G.1]; 5 [2.G.2]; 6 [Foundation] SMP1, 4–7; 2.MD.7 SMP1, 2, 4–6; 2.OA.2, 2.NBT.5, 2.NBT.7, 2.MD.7 SMP2, 4, 6, 7; 2.MD.6 SMP1, 3–8; 2.NBT.5, 2.NBT.7 Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 35 125 Copyright © The McGraw‐Hill Companies, Inc. Getting Started: Mental Math and Reflexes [2.OA.2] Division from Multiplication To guide children as they review multiplication/division fact families, and investigate the relationship between multiplication and division. Graphs: Comparing Speeds of Animals and People 126 127 To provide experience with reading, creating, and interpreting bar graphs; and to guide children as they find the range and middle value (median) of a data set. The Mode of a Set of Data To guide children as they organize a set of data with a line plot and frequency table, display a set of data with a bar graph, and identify the median and mode. Progress Check 12 128 To assess children’s progress on mathematical content through the end of Unit 12. Part 1: Focuses on the relationship between multiplication and division. Part 2: Game: Addition Card Draw [2.NBT.6] Math Boxes: [ 12-5↔12-7↔12-8]; 1 [2.NBT.8]; 2 [Maintain]; 3 [2.G.3]; 4 [Foundation]; 5 [2.MD.7]; 6 [2.NBT.5] SMP1, 2, 4–6, 8; 2.OA.2 Part 1: Focuses on organizing and interpreting data on a bar graph. [2.MD.10] Part 2: Math Boxes: [ 12-6↔12-2↔12-4]; 1 [2.MD.10]; 2 [2.NBT.5]; 3 [2.NBT.4]; 4 [2.G.1]; 5 [2.G.2]; 6 [Foundation] Home Link: [2.MD.10] Part 3: Enrichment and Extra Practice [2.MD.10] SMP2, 4–7; 2.MD.10 Part 1: Focuses on displaying data in line plots and bar graphs and on finding the mode and median. [2.MD.9, 2.MD.10] Part 2: Game: Addition Card Draw [2.NBT.6] Math Boxes: [ 12-7↔12-5↔12-8]; 1 [2.NBT.8]; 2 [Maintain]; 3 [2.G.3]; 4 [Foundation]; 5 [2.MD.7]; 6 [2.NBT.5] Home Link: [2.MD.10] Part 3: Extra Practice [2.MD.9] Part 1: Checks children’s progress at the end of Unit 12. Part 2: Math Boxes: [ 12-8↔12-5↔12-7]; 1 [2.NBT.8]; 2 [Maintain]; 3 [2.G.3]; 4 [Foundation]; 5 [2.MD.7]; 6 [2.NBT.7, 2.NBT.9] SMP2, 4–6; 2.MD.9, 2.MD.10 * Visit www.everydaymath.com for Guiding Questions that support Standards for Mathematical Practice (SMPs). Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 36 Common Core State Standards for Grade 2** OPERATIONS AND ALGEBRAIC THINKING 2.OA Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Add and subtract within 20. 2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. Work with equal groups of objects to gain foundations for multiplication. 2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. NUMBER AND OPERATIONS IN BASE TEN 2.NBT Understand place value. 2.NBT.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases. 2.NBT.1a. 100 can be thought of as a bundle of ten tens ---- called a ‘‘hundred.’’ 2.NBT.1b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s. 2.NBT.3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 37 Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations. 2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8. Mentally add 10 or 100 to a given number 100--900, and mentally subtract 10 or 100 from a given number 100--900. 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. MEASUREMENT AND DATA 2.MD Measure and estimate lengths in standard units. 2.MD.1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3. Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. Work with time and money. 2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 38 Represent and interpret data. 2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. GEOMETRY 2.G Reason with shapes and their attributes. 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 39 Standards for Mathematical Practice** 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, ‘‘Does this make sense?’’ They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize----to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents----and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and----if there is a flaw in an argument----explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 40 4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. 5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. 6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 -- 3(x -- y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 41 8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y -- 2)/(x -- 1) = 3. Noticing the regularity in the way terms cancel when expanding (x -- 1)(x + 1), (x -- 1)(x2 + x + 1), and (x -- 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. **© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Grade 2 Everyday Mathematics® Common Core Instructional Planning and Pacing Guide p. 42
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