# 2nd Grade Mathematics Curriculum Guide by accinent

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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

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