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Introduction to 1st Grade Curriculum Guide for Mathematics The following guide is a suggested sequence for mathematics instruction for the 2007-2008 school year and addresses the current Alabama Course of Study objectives with the exception of Al COS objectives #4, 11, and 12. Options for addressing these 3 objectives are listed below: AL COS #4 Identify parts of a whole with two, three, or four equal parts. Integrate this objective into daily living activities such as sharing materials or math manipulatives, passing out different kinds of snack, or dividing the class into groups. Story problems offer an additional opportunity for children to think about dividing situations. Ex. – We are having pizza at our Valentines Day party. If we have one pizza for every four people, how many slices can each person have? (There are 8 slices per pizza.) AL COS #11 Identify the hour and half hour using analog and digital clocks. (Opportunities to explore time are described in the Routines section of Investigations.) AL COS #12 Locate days, dates, and months on a calendar. (Additional opportunities to explore the calendar are described in the Routines section of Investigations.) Incorporate this standard into the daily routine of your classroom with questions such as, “What is the date for Labor Day? How many days before we are out for Spring Break? ___________’s birthday is on October 14. What day will of the week will that be?” Write the date on the board each day as a class. Problem Solving Solving mathematical problems in the real world is the heart of math instruction in first grade. Children are easily engaged in solving problems that relate to their experiences at home and school. Although Investigations includes some opportunities for children to solve story problems, teachers are encouraged to incorporate additional problem solving opportunities for their children as a regular math class routine. Resources for story problems are Marilyn Burns’ Math and Literature, Grade K-1, Math And Nonfiction: Grades K-2 (Math and Nonfiction) by Jamee Petersen, Math and Literature (K-3), Book One by Marilyn Burns, and Math and Literature (K-3), Book Two by Stephanie Sheffield. How Do You Know When to Ask Questions and When to Tell? The very heart of mathematics is logical reasoning and the study of relationships. Students need opportunities to investigate, ponder, and reason about relationships between numbers, computation strategies, and the big ideas of mathematics. The majority of your math instruction will consist of asking students questions to help them build understanding of mathematical ideas and how and why they work. If it is possible for students to figure something out then, “Ask, don’t tell” is a good rule of thumb to use. However, several of the AL COS objectives can be readily classified as Social Knowledge –knowledge that is not built on relationships but is learned through telling. Examples of Social Knowledge are: vocabulary terms, rules for how to write an equation, how to organize a graph, the order for the days of the week, etc. Since this type of knowledge is not possible to figure out, students need to be told this information. The following chart lists each first grade AL COS objective and provides information about when to ask questions and when to tell. Draft –May 24, 2007 1st Grade Math Curriculum Guide AL COS Objective Ask Questions For: Tell: #1 Demonstrate concepts of Understanding that the quantity Meaning of vocabulary number sense by counting remains the same when the spacial such as plus, minus, forwards and backwards by 1’s, arrangement changes. equal, all, and none. 2’s, 5’s, and 10’s up to 100; Understanding the value of a The meaning and use of counting forward and backward number and how it relates to other symbols such as +, -, =, from an initial number other than numbers <, > 1; and using multiple Determining the value of a number Identifying the place representations for a given that is 10 more or 10 less than a value of a digit in the number. given number. ones place or tens place Understanding of skip counting by in a number. 2’s, 5’s, and 10’s. Determining the monetary value of individual coins. #2 Demonstrate conceptual Developing increasingly efficient How to read and write understanding of addition and strategies for addition equations subtraction by telling number Developing beginning Vocabulary terms stories; joining separating, and understanding of subtraction and comparing sets of objects; and at least one strategy for solving applying signs (+ and -) to the subtraction problems actions of joining and separating sets. #3 Demonstrate conceptual fluency of basic addition and subtraction facts by identifying sums to 10 and differences with minuends of 10 or less. #4 Identify parts of a whole with 2, 3, or 4 equal parts. #5 Create repeating patterns. Identifying and continuing patterns. Developing a rule to show how a pattern grows. #6 Solve problems using the Understanding of zero and how it NOTE: It is not necessary identity and commutative affects a total. for children to know the properties of addition. Understanding that the order of names of these properties to sets does not affect the total. use them. #7 Demonstrate relationships Finding combinations of numbers How to read and write between operations. Relationship between a known equations sum and a related subtraction problem Draft –May 24, 2007 1st Grade Math Curriculum Guide #8 Differentiate among plane Describing similarities among Geometric vocabulary shapes, including circles, plane and solid shapes. squares, rectangles, and Transferring shape combinations triangles. from one representation to another (Ex. from blocks to a drawing) #9 Identify solid shapes in the Recognizing real-life examples of environment, including cubes, line symmetry. rectangular prisms, cones, Combining shapes to fill in the spheres, and cylinders. area of a given shape. #10 Compare objects according Measuring with nonstandard units Names for units of to length, weight, and capacity. measurement #11 Identify the hour and half Relationship between numbers on Vocabulary associated hour using analog and digital the clock and 5, 30, and 60 with time clocks minutes How many minutes in an hour How clocks work #12 Locate days, dates, and Understanding of cyclical nature Names for days of the months on a calendar. of measurement of time. week and months of the year How many days in work week and full week Vocabulary such as yesterday, today, tomorrow, day before, day after #13 Organize object or Analyzing and reporting data Vocabulary information into predetermined and labeled data displays, including pictographs, tally charts, bar graphs, or double- loop Venn diagrams. Number Talks Number Talks are included in this guide, because they are viewed as an integral part of mathematics instruction. Ten to 15 minutes of classroom number talks 3 to 4 times a week help students develop computation fluency with mental math. Number Talks provide opportunities to specifically address Al COS objectives #s 1, 2, 3, 6, & 7. Using smaller numbers allows students to grapple with the number relationships and conceptual understanding of the operations. Number Talks may be organized in a whole-class setting and/or a small group of students with a concentrated focus on their specific needs. For example, if several students have begun thinking using known sums to solve addition problems, you could pull them together for a number talk that targets this need. Likewise, if a group of students is continuing to count all, you would pull them for a concentrated number talk designed to build upon and extend this strategy. Draft –May 24, 2007 1st Grade Math Curriculum Guide 1st Grade Mathematics Curriculum Guide 1st Nine Weeks (August 9 – October 12) August 9-31 (17 days) September 4-28 (19 days) October 1-12 (8 days) Strand Overview of all strands Number: Addition Number: Addition Number: Counting, Addition Data Analysis - MMI Data Analysis - MMI Data Analysis - MMI Patterns & Algebraic Thinking. Patterns & Algebraic Thinking Patterns & Algebraic Thinking Big Idea *Number Sense & Logic *Number Sense & Logic *Number Sense & Logic *Flexibility with numbers – *Flexibility with numbers - *Flexibility with numbers – composing and decomposing composing and decomposing composing and decomposing numbers numbers numbers * Counting - about 20 objects * Counting - about 20 objects * Counting - about 20 objects **Fluency to 6 *Fluency to 6 **Doubles to 12 *Comparing numbers - more/less *Counting - about 40 objects **Skip counting *Describing, predicting, *Finding combinations of numbers *Finding combinations of numbers and constructing a pattern up to about 15 up to about 15 *Combining single digit numbers *Representing same pattern in *Developing and recording *Developing and recording different ways strategies for combining story strategies for combining story *Developing and recording strategies problems problems for combining story problems Primary Mathematical Thinking (TERC) First Grade Math (Bachman)- Building Number Sense (cont.) Resources Invest. 1 (sessions 1-4) Patterns p. 39-55 (5 days) (TERC) Invest. 2 (sessions 1-6) Mathematical Thinking (TERC) Invest 2 (sessions 7-9) (3 days) Invest. 3 (sessions 1-6) Investigations 4 (sessions 4-6)(3 days) Invest 3 (sessions 1-5) (5 days) Building Number Sense (TERC) Invest. 1- Combine sessions 1-2, do sessions 3 & 4, omit sessions 5&6, combine sessions 7-8; do session 9 (5 days) Invest. 2 (sessions 1-6) (6 days) Data MMI Data Collection MMI Data Collection MMI Data Collection Resources Pattern Kathy Richardson's Growing Kathy Richardson's Growing Kathy Richardson's Growing Resources Patterns (1-2 per month) Patterns (1-2 per month) Patterns (1-2 per month) AL COS AL COS #1, 2, 3, 5,12, 13 AL COS #1, 2, 3, 12, 13 AL COS #1, 2, 3, 5, 12, 13 Objectives # Talk Focus Strategies for combining Strategies for combining numbers - Strategies for combining numbers numbers - counting all, counting counting all, counting on, using - counting all, counting on, using on, using known sums known sums, One more, known sums, compensation One more Becoming familiar with single-digit One more & one less addition pairs Becoming familiar with single-digit Finding groups when counting addition pairs Doubles to 12 Finding groups when counting # Talk Tools Rekenrek, Quick Images, bead Tens Frame for days in school, Tens Frame for days in school, strings, build a number rekenrek, Quick Images, bead number strings, rekenrek, Quick strings, build a number Images, bead strings, build a # Games Addition sums to10/ Addition sums to 12 - Punta, path Addition sums to 12 – Double Comparing numbers –50 chips, games with two 1-6 dice, the Sorry, Double Trouble, Dice Trick path games with 0-5 dice, path Balance Game, Shut the Box, Magic (for 7), All but Seven, Doubles games with one die +1, One Circle, Guess My Number, 10 or Cover Up, Spider Legs More, War (or Compare w/ Bust, Counters in a Cup, Double cards), Cover Up and Uncover, War (or Double Compare), rekenrek Speed Assessments Fluency, Problem Solving, Observation of math games Observation of math games st Computation Benchmark 1 story problem MMI 1 Quarter Problem Assess. (August 20-31) Solving Task Draft –May 24, 2007 1st Grade Math Curriculum Guide 1st Grade Mathematics Curriculum Guide 2nd Nine Weeks (October 15-December 19) October 15-31 (13 days) November 1-30 (18 days) December 3-19 (13 days) Strand Number: Counting, Addition Number: Addition Number: Addition Data Analysis - MMI Data Analysis - MMI Data Analysis - MMI Patterns & Algebraic Thinking Patterns & Algebraic Thinking Patterns & Algebraic Thinking Big Idea *Number Sense & Logic *Number Sense & Logic *Number Sense & Logic *Flexibility with numbers – *Flexibility with numbers - *Flexibility with numbers – composing and decomposing composing and decomposing composing and decomposing numbers numbers numbers * Counting - about 20 objects **Skip Counting **Doubles to 12 **Doubles to 12 **Doubles to 12 **Skip counting **Skip counting *Using an attribute for sorting *Finding combinations of numbers *Finding combinations of *Gathering, sorting, recording, and up to about 15 numbers up to about 15 keeping track of data * Gathering, sorting, recording, *Developing and recording *Developing and recording and keeping track of data strategies for combining story strategies for combining & *Explaining, interpreting, and problems separating story problems presenting data to others *Developing and recording strategies for combining & separating story problem Primary Continue Building Number Survey Questions and Secret Rules Survey Question and SecretRules Resources Sense Invest 1 (session 1-6) (6 days) Invest 4 (session4-5) (2 days) (TERC) Invest 2 (session 1-6) (6 days) Developing Number Concepts: Invest 3 (sessions 6-9) (3 days) Invest 3 (session 1-3) (3 days) Addition and Subtraction - Kathy Invest 4 (sessions 1-10) (10 days) Invest 4 (session 1-3) (3 days) Richardson (11 days) Survey Questions and Secret Rules to be spread over the months of Nov. and Dec. with opportunities to work with number intertwined with this unit as there are not many in the TERC unit itself. Data MMI Data Collection MMI Data Collection MMI Data Collection Resources Pattern Kathy Richardson's Growing Kathy Richardson's Growing Kathy Richardson's Growing Resources Patterns (1-2 per month) Patterns (1-2 per month) Patterns (1-2 per month) AL COS Objectives AL COS #1, 2, 3, 5,12, 13 AL COS #1, 2, 3, 12, 13 AL COS #1, 2, 3, 5, 6, 12, 13 # Talk Focus Strategies for combining Strategies for combining numbers - Strategies for combining numbers numbers - counting all, counting counting all, counting on, using - counting all, counting on, using on, using known sums, using known sums, using friendly known sums, using friendly friendly numbers (doubles, 5’s, numbers (doubles, 5’s, 10’s) numbers (doubles, 5’s, 10’s) 10’s) One more & one less One more & one less One more & one less Becoming familiar with single-digit Becoming familiar with single-digit Becoming familiar with single- addition pairs addition pairs digit addition pairs Doubles to 12 Doubles to 12 Doubles to 12 Finding groups when counting Finding groups when counting Finding groups when counting # Talk Tools Tens Frame for days in school, Tens Frame for days in school, Tens Frame for days in school, number strings, rekenrek, Quick number strings, rekenrek, number strings, rekenrek, Images, bead strings, build a Quick Images, bead strings, build a Quick Images, bead strings, build number number a number Games Addition sums to 12 – path Addition sums to 12 – Doubles +1 Addition sums to 12– new path games with number dice (not Cover Up, Chutes and Ladders games with new dice available dots), Doubles Cover Up, 5+ (either double spinner or use dice Bingo, Go Fish for 10’s Assessments Observation of math games Observation of math games Observation of math games nd Fluency, Computation MMI 2 Quarter Problem Benchmark Assessment (Nov.1-16) Solving Task Draft –May 24, 2007 1st Grade Math Curriculum Guide 1st Grade Mathematics Curriculum Guide 3rd Nine Weeks (January 3-March 10) January 3-31 (20 days) February 1-29 (20 days) March 3-10 (6 days) Strand Number: Counting, Addition Number: Addition Number: Addition Data Analysis - MMI Data Analysis - MMI Data Analysis - MMI Patterns & Algebraic Thinking Patterns & Algebraic Thinking. Patterns & Algebraic Thinking Geometry Geometry Big Idea *Number Sense & Logic *Number Sense & Logic *Number Sense & Logic *Adding single-digit numbers to *Adding single-digit numbers *Adding two or more single-digit about 12 *Flexibility with numbers numbers *Flexibility with numbers *Flexibility with numbers **Doubles to 14 **Doubles to 12 **Doubles to 12 *Observing, describing, and *Finding combinations of numbers *Observing, describing, and comparing 2-D and 3-D shapes. up to about 20 comparing 2-D and 3-D shapes. *Using rotation and reflection to *Finding the total of several 2’s, *Using rotation and reflection to arrange shapes 4’s, 5’s, or 10’s arrange shapes *Noticing relationships between *Becoming familiar with coins and *Noticing relationships between shapes equivalencies among them shapes *Read, write, and sequence numbers to 100 * Developing and recording strategies for combining & separating story problems Primary Quilt Squares and Block Towns Quilt Squares and Block Towns Number Games and Story Resources (TERC) (TERC) (continued) Problems (TERC) - sessions that Invest 1 (session 1-15) (15 days) Invest 2 (session 5-10) (10 days) extend over several days can Invest 2 (session 1-5) (5 days) Invest 3 (session 1-7) (7 days) usually be done in less time (6days) During this unit, it is often beneficial to play math games that deal with number and/or have number talks after working on geometry for 30-40 min. of math time Data MMI Data Collection MMI Data Collection MMI Data Collection Resources Pattern Kathy Richardson's Growing Kathy Richardson's Growing Kathy Richardson's Growing Resources Patterns (1-2 per month) Patterns (1-2 per month) Patterns (1-2 per month) AL COS AL COS #1, 2, 3, 5, 6, 8, 9, 12, 13 AL COS #1, 2, 3, 6, 8, 9, 12, 13 AL COS #1, 2, 3, 5, 6, 12, 13 Objectives # Talk Focus Strategies for combining Strategies for combining numbers - Strategies for combining numbers numbers - counting on, using counting on, using known sums, - counting on, using known sums, known sums, using friendly using friendly numbers(doubles, 5’s, using friendly numbers (doubles, numbers (doubles, 5’s, 10’s), 10’s), compensation 5’s, 10’s), compensation compensation Becoming familiar with single-digit Becoming familiar with single-digit Becoming familiar with single-digit addition pairs addition pairs addition pairs Doubles to 14 Doubles to 16 Doubles to 12 Doubles +1 Finding groups when counting Tens Combinations Tens Combinations Tens Combinations # Talk Tools Tens Frame for days in school, Tens Frame for days in school, Tens Frame for days in school, number strings, rekenrek, Quick number strings, rekenrek, number strings, rekenrek, Images, bead strings, build a Quick Images, bead strings, build a Quick Images, bead strings, build number number a number Games Total Tens, 21, Tens with Cards, Tic Tac 12, Toujours 12, Make 10, Uncover 12 Choose, Boardwalk Jenga Nickelodeon, Total of 10, Foxes Boxes, Sneaky Snake, Dot Addition, Five in a Row, Tens Concentration Assessments Observation of math games Observation of math games Observation of math games rd Fluency, Computation MMI 3 Quarter Problem Benchmark Assessment (Feb.1-15) Solving Task Draft –May 24, 2007 1st Grade Math Curriculum Guide 1st Grade Mathematics Curriculum Guide 4th Nine Weeks (March 11-May 22) March 11-31 (10 days) April 1-30 (20 days) May 1-22 (16 days) Strand Number: Counting, Addition Number: Addition Number: Addition Data Analysis - MMI Data Analysis - MMI Data Analysis - MMI Patterns & Algebraic Thinking Patterns & Algebraic Thinking. Patterns & Algebraic Thinking Probability Money Measurement Big Idea *Number Sense & Logic *Number Sense & Logic *Number Sense & Logic *Adding two or more single-digit *Adding single-digit numbers *Adding two or more single-digit numbers *Flexibility with *Subtract with minuends of 10 or numbers *Flexibility with numbers numbers less **Doubles to 20 **Doubles to 16 *Flexibility with numbers *Finding combinations of numbers *Finding combinations of **Doubles to 18 up to about 20 numbers up to about 20 *Finding combinations of numbers *Compare weights of objects and *Finding the total of several 2’s, up to about 20 represent the results of the 4’s, 5’s, or 10’s *Finding the total of several 2’s, 4’s, comparison *Becoming familiar with coins 5’s, or 10’s *Measure capacity using and equivalencies among them *Becoming familiar with coins and nonstandard units *Read, write, and sequence equivalencies among them *Measure and compare lengths numbers to 100 *Read, write, and sequence * Developing and recording numbers to 100 strategies for combining & * Developing and recording separating story problems strategies for combining & *Demonstrate relationships separating story problems among the operations Primary Number Games and Story Number Games and Story Bigger, Taller, Heavier, Smaller Resources Problems (TERC) - sessions Problems (TERC) - sessions that (TERC) – This unit combines well that extend over several days extend over several days can with the Balancing and Weighing can usually be done in less time usually be done in less time unit in science. (5 days) (14 days) (16 days) Marilyn Burns Probability Marilyn Burns Money Likely and Unlikely Coins and Magnifiers, The Matching Roll Two Dice Investigation Game, Money in the Bank (5 days) (5 days) Data MMI Data Collection MMI Data Collection MMI Data Collection Resources Pattern Kathy Richardson's Growing Kathy Richardson's Growing Kathy Richardson's Growing Resources Patterns (1-2 per month) Patterns (1-2 per month) Patterns (1-2 per month) AL COS Objectives AL COS #1, 2, 3, 5, 6, 12, 13 AL COS #1, 2, 3, 6, 7, 8, 9, 12, 13 AL COS #1, 2, 3, 5, 6, 10, 12, 13 # Talk Focus Strategies for combining numbers - Strategies for combining numbers - Strategies for combining numbers - counting on, using known sums counting on, using known sums counting on, using known sums (doubles, 5’s, 10’s), compensation (doubles, 5’s, 10’s), compensation (doubles, 5’s, 10’s), compensation Becoming familiar with single-digit Becoming familiar with single-digit Becoming familiar with single-digit addition pairs addition pairs addition pairs Doubles to 16 Doubles to 20 Finding groups when counting Doubles to 18 Finding groups when counting Compensation Doubles +1 Compensation Tens Combinations Tens Combinations Tens Combinations # Talk Tools Tens Frame for days in school, Tens Frame for days in school, Tens Frame for days in school, number strings, rekenrek, Quick number strings, rekenrek, number strings, rekenrek, Images, bead strings, build a Quick Images, bead strings, build a Quick Images, bead strings, build number number a number Games Uncover 12 Choose, Australian 31, 15 Numbers, Racko, Salute Nickelodeon, Total of 10, Foxes Tens Concentration Boxes, Sneaky Snake, Dot Addition, Five in a Row Assessments Observation of math games Observation of math games Observation of math games th Fluency, Problem Solving, MMI 4 Quarter Problem Computation Benchmark Assess. Solving Task (April 21-May 2) Draft –May 24, 2007 1st Grade Math Curriculum Guide Draft –May 24, 2007 1st Grade Math Curriculum Guide