K-2
During the early years in a curriculum designed to develop number sense, students read, write, and count using whole numbers. They represent whole numbers using concrete, pictorial, and symbolic representations. They recognize different representations for whole numbers and explain why those representations are the same. They compare and order whole numbers and
use a variety of strategies to estimate quantities.

The basic understanding of place value forms the foundation for subsequent work with number.
Students group objects recognizing that digits have different values depending upon their placement
or position in numerals.

3-5
Youngsters in grades 3-5 represent whole numbers, fractions, and decimals with concrete objects, pictures, and symbols in a variety of contexts. They recognize equivalent fractions and decimals and explain the basis for the equivalence. They compare and order fractions and decimals. They understand and use the place value system and various properties of numbers, including the properties of special numbers like 0 and 1; round numbers to a specified precision; and reasonably estimate answers to
computations.

Students use a variety of tools to model operations with whole numbers, develop methods for recording operations, and relate models to standard symbolic expressions and algorithms. They further develop
and apply different methods of computing, such as mental computation, paper-and-pencil algorithms,
and technology. They learn the fundamental order of operations and explore various properties of operations.

Students use a variety of strategies for learning basic multiplication and division facts. They explain why such strategies work by modeling using counters or other tools. Overall, students have a firm foundation in the understanding of place value, quickly recall basic addition, subtraction, multiplication, and division facts, and easily carry out operations with whole numbers.

6-8
Students in the middle years represent integers, rational numbers, and irrational numbers using concrete objects, pictures, and symbols in a variety of contexts. They explore relationships among rational numbers and recognize equivalence for fractions, decimals, and percents and explain the basis for the equivalence. They extend understanding of place value to decimal and scientific notation. They recognize properties of integers, rational, and some real numbers, including 0,1, and inverses. They express numerical comparisons as ratios and rates and solve problems using ratio, proportion, and percent.

Students understand number theory relationships including prime and composite numbers, factors, and multiples. They explain the meaning of powers and square roots of numbers, develop facility with estimation and mental computation involving square numbers, use calculators to compute powers and roots, and can apply the laws of exponents in problem situations.
 
 
 
 

Kindergarten

Goal 1: The learner will recognize, model, and write numbers through
10.

- 1.01 Model numbers in a variety of ways.
- 1.02 Read, write and count using whole numbers; rote count forward to 30 or beyond and
               backward from 10.
- 1.03 Use 1-1 correspondence to identify how many (0 - 10).
- 1.04 Recognize numerals and match to sets 0 - 10.
- 1.05 Write numerals 0-9 in meaningful contexts.
- 1.06 Use ordinals first through fifth.
- 1.07 Create and identify sets with more, less, or equal members by matching.
- 1.08 Combine and remove objects from sets, describe results.
- 1.09 Estimate quantities less than 20.
- 1.10 Create and solve story problems within a group.
- 1.11 Share equally (divide) between two people; explain solution.
 

First
Goal 1: The learner will read, write, and model numbers through 100
and compute with whole numbers.

- 1.01Count using one-to-one correspondence to 30.
- 1.02Rote count by 1's, 5's and 10's to 100; by 2's to 20.
- 1.03Make sets and match numerals up to 30.
- 1.04Compare and order sets and numerals up to 30.
- 1.05Read and write numerals to 100.
- 1.06Read number words zero to ten.
- 1.07Use ordinal numbers first through tenth.
- 1.08Group and count objects by 2's, 5's, and 10's.
- 1.09Identify one more/less/before/after/between.
- 1.10Identify equal and unequal numerals and sets.
- 1.11Represent numbers in a variety of ways: using tallies, building models to 100.
- 1.12 Estimate quantities up to 30. Recognize when solutions to problems are reasonable.
- 1.13 Group objects into tens and ones, recognize models; record.
- 1.14 Model concept of addition; know the combinations for sums to 10.
- 1.15 Model concept of subtraction as take-away, comparison, and missing addends.
- 1.16 Model the division of sets into two, three or four equal parts; explain solution.
- 1.17 Relate addition and subtraction to symbolic notation and write equations.
- 1.18 Find sums and differences using counting strategies such as counting on and counting back.
- 1.19 Memorize addition and subtraction facts to 10.
- 1.20 Model 10 more/less to 100.
- 1.21 Model 2-digit addition/subtraction with multiples of 10 to 100.
- 1.22 Create and solve problems using addition and subtraction. Use problem-solving strategies:
        modeling with manipulative, acting out, drawing, using diagrams; use calculators as
        appropriate. Explain solutions.
 

Second
Goal 1: The learner will read, write, and model numbers through 1000,
and compute with numbers less than 1000.

- 1.01 Rote count up to 1000.
- 1.02 Identify and use 10 more and 10 less.
- 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
- 1.04 Read word names for numbers to 100.
- 1.05 Use counting strategies such as skip counting by 2's, 5's, and 10's and grouping objects by
               3's and 4's.
- 1.06 Identify odd and even numbers using objects.
- 1.07 Group objects into ones, tens, and hundreds and record in standard form.
- 1.08 Model 3-digit numbers; identify, read, and write correct numerals.
- 1.09 Indicate the value of each digit in any 2 or 3-digit number.
- 1.10 Use problem-solving strategies such as diagrams, organized lists, manipulatives, act out,
              guess and check, pictures; use calculators when appropriate.
- 1.11 Explain solutions to problems using words, pictures, and numbers.
- 1.12 Make reasonable estimates up to 100 objects.
- 1.13 Identify missing addends for addition facts to 18.
- 1.14 Add 3 single-digit numbers.
- 1.15 Model 2-digit addition and subtraction using manipulatives and alternative strategies; record,
               and explain.
- 1.16 Memorize addition/subtraction facts up to 18.
- 1.17 Add 2- and 3- digit numbers with and without regrouping.
- 1.18 Use addition/subtraction strategies to solve problems.
- 1.19 Divide regions/sets into halves, thirds, and fourths. Record in fractional form.
- 1.20 Model repeated addition (multiplication) and sharing equally (division); record solutions.

Third
Goal 1: The learner will model, identify and compute with numbers less
than 10,000.

- 1.01 Read and write word names for numbers to 1,000.
- 1.02 Relate standard and expanded notation to 3- and 4-digit numbers.
- 1.03 Compare and order numbers less than 10,000.
- 1.04 Use estimation techniques in determining solutions to problems.
- 1.05 Identify odd and even numbers; generalize ways to determine odd or even.
- 1.06 Model fractions and mixed numbers using regions and sets; describe relationships of parts
        to whole; record.
- 1.07 Compare and order fractions using models; describe comparisons.
- 1.08 Model equivalent fractions using manipulatives and pictures.
- 1.09 Subtract 2- and 3-digit numbers.
- 1.10 Model and explain multiplication in a variety of ways including repeated addition, rectangular
         arrays and skip counting.
- 1.11 Model and use the identity and commutative properties for addition and multiplication.
- 1.12 Model and explain division in a variety of ways including sharing equally, repeated subtraction,
              rectangular arrays, and its relationship to multiplication.
- 1.13 Memorize multiplication facts/tables through 10.
- 1.14 Determine if there is sufficient information to solve a problem; identify missing or extraneous
               data in problem-solving situations.
- 1.15 Solve meaningful, multi-step problems involving addition, subtraction and multiplication using
               a variety of strategies; use calculators as appropriate

Fourth
Goal 1: The learner will read, write, model, and compute with rational
numbers.

- 1.01 Read and write numbers less than one million using standard and expanded notation.
- 1.02 Use estimation techniques in determining solutions to problems.
- 1.03 Model and identify the place value of each digit in a multi-digit numeral to the hundredths
              place.
- 1.04 Model, identify, and compare rational numbers (fractions and mixed numbers).
- 1.05 Identify and compare rational numbers in decimal form (tenths and hundredths) using
             models and pictures.
- 1.06 Relate decimals and fractions (tenths and hundredths) to each other using models and
               pictures.
- 1.07 Use models and pictures to add and subtract decimals, explaining the processes and
              recording  results.
- 1.08 Use models and pictures to add and subtract rational numbers with like denominators.
- 1.09 Find the fractional part of a whole number using models and pictures.
- 1.10 Model and explain associative and distributive properties.
- 1.11 Memorize the division facts related to the multiplication facts/tables through 10.
- 1.12 Identify missing factors in multiplication facts.
- 1.13 Round rational numbers to the nearest whole number and justify.
- 1.14 Estimate solutions to problems.
- 1.15 Multiply 2- or 3- digit numbers by 1-digit numbers or a 2-digit multiple of 10.
- 1.16 Divide using single-digit divisors, with and without remainders.
- 1.17 Use order of operations with addition, subtraction, multiplication, and division.
- 1.18 Solve multi-step problems; determine if there is sufficient data given, then select additional
         strategies including:
         make a chart or graph
         look for patterns
         make a simpler problem
         use logic
         work backwards
         break into parts.
         Verify and interpret results with respect to the original problem; use calculators as appropriate.
         Discuss alternate methods for solution.

Fifth
Goal 1: The learner will understand and compute with rational numbers.

- 1.01 Use place value through millions in real-world situations including reading, writing,
         estimating, and comparing numbers in a variety of forms.
- 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
- 1.03 Relate exponential notation to repeated multiplication.
- 1.04 Estimate and solve division problems with 2- and 3- digit divisors; explain solution.
- 1.05 Use the order of operations to simplify numerical expressions.
- 1.06 Find multiples, common multiples, and least common multiple of numbers; explain.
- 1.07 Find the factors, common factors, and greatest common factor of numbers; explain.
- 1.08 Identify prime and composite numbers less than 100.
- 1.09 Identify equivalent decimals and fractions at the symbolic level. Explain the equivalence.
- 1.10 Compare and order numbers with decimals to the thousandths place; explain solution.
- 1.11 Compare and order fractions which are given with the same numerators or the same
        denominators; explain solution.
- 1.12 Add and subtract fractions with like denominators.
- 1.13 Multiply a fraction by a whole number.
- 1.14 Use models and pictures to add and subtract fractions and mixed numbers with unlike
              denominators; record solutions.
- 1.15 Estimate results and compute sums and differences with decimal numbers.
- 1.16 Use models and pictures to multiply a whole number by a decimal number; record and
               explain.
- 1.17 Determine if there is sufficient information to solve a problem; identify missing or extraneous
               data in problem-solving situations.
- 1.18 Solve multi-step problems using an organized approach, and selecting additional strategies
               including:
               restate the problem
               classify lists
               write a number sentence
               Verify and interpret results with respect to the original problem; use calculators as appropriate.

Sixth
Goal 1: The learner will understand and compute with rational numbers.

- 1.01Read, write and make models of numbers including percents and
              exponential.
- 1.02 Relate fractions, decimals, and percents.
- 1.03 Compare and order fractions, decimals, and percents.
- 1.04 Multiply and divide fractions, mixed numbers, and decimals using models and pictures;
               record solution.
- 1.05 Multiply and divide fractions, mixed numbers, and decimals.
- 1.06 Add and subtract fractions and mixed numbers with unlike denominators.
- 1.07 Use estimation and mental math to solve problems with fractions, decimals, and percents;
               explain solution.
- 1.08 Solve problems using prime factorization, common factors and common multiples. Explain
               solutions.
- 1.09 Use models and pictures to relate concepts of ratio, proportion, and percent; record results.
- 1.10 Use models and pictures to demonstrate understanding of integers. Record results.
- 1.11 Compare and order integers.- 
- 1.12 Use the order of operations to simplify numerical expressions with parentheses and exponents.

- 1.13 Translate word problems into number sentences and solve. Explain solutions.
- 1.14 Analyze problem situations, determine if there is sufficient information to solve the problem, identify
        missing or extraneous data, select appropriate strategies, and use an organized approach to solve
        multi-step problems; use calculators when appropriate.

Children’s Literature

K~
Adams, Pam. There Were Ten in The Bed. 1979.
~ This book focuses on counting in the reverse order by starting out with ten in the bed and all of the babies rolled out until there was only one baby left sleeping peacefully in the bed.
? 1.01 Model numbers in a variety of ways.
? 1.02 Read, write and count using whole numbers; rote count forward to 30 or beyond and
               backward from 10.
? 1.03 Use 1-1 correspondence to identify how many (0 - 10).
? 1.04 Recognize numerals and match to sets 0 - 10.
? 1.05 Write numerals 0-9 in meaningful contexts.

Anno, Mitsumasa. Anno’s Counting Book. 1975.
~ This book focuses on the counting numbers 1-12. It includes visual representations of each number with each page containing that number of blocks and the number written on the opposite side of the page. Each number is represented in the picture several times. Ex. 5 cats, 5 buildings, 5 trees. 5 cars.  This book has no words, it is only a visual representation.
? 1.01 Model numbers in a variety of ways.
? 1.02 Read, write and count using whole numbers; rote count forward to 30 or beyond and
               backward from 10.
? 1.03 Use 1-1 correspondence to identify how many (0 - 10).
? 1.04 Recognize numerals and match to sets 0 - 10.
? 1.05 Write numerals 0-9 in meaningful contexts.

Carter, David. How Many Bugs in a Box.1988.
~ This book is a counting book for the numbers 1-10. This book is a great asset because of the colorful pictures, that pop up. Each box has a number of bugs in it from 1-10 and also gives a description of what kinds of bugs they are.
? 1.01 Model numbers in a variety of ways.
? 1.02 Read, write and count using whole numbers; rote count forward to 30 or beyond and
               backward from 10.
? 1.03 Use 1-1 correspondence to identify how many (0 - 10).
? 1.04 Recognize numerals and match to sets 0 - 10.
? 1.05 Write numerals 0-9 in meaningful contexts

McGrath, Barbara. Bolster, Rob & Mazzola, Frank; illus. The Cheerios Counting Book.1998
 ~ This book is great because it will give you the number, spell it out, and then uses the number in
 a sentence. Ex. #6 six cheerios, and six apples.
This book skips number 11-19, but visualizes them by showing the number and writing out the word. The book also uses the 10 number as it root because it goes by tens from 20-100 and then zero is placed at the end of the book since zero is so confusing for children.
? 1.01 Model numbers in a variety of ways.
? 1.02 Read, write and count using whole numbers; rote count forward to 30 or beyond and
               backward from 10.
? 1.03 Use 1-1 correspondence to identify how many (0 - 10).
? 1.04 Recognize numerals and match to sets 0 - 10.
? 1.05 Write numerals 0-9 in meaningful contexts
Noll, Sally. Off and Counting. 1984.
~ This book is a early years counting book. The book goes through #’s 1-10 and has pictures to represent each number. This book is good because it has every number clearly represented, in both boldly written words and brightly colored pictures.
? 1.01 Model numbers in a variety of ways.
? 1.03 Use 1-1 correspondence to identify how many (0 - 10).
? 1.04 Recognize numerals and match to sets 0 - 10.
? 1.05 Write numerals 0-9 in meaningful contexts

First
Aker, Suzanne. Karlin, Bernie; illus. What comes in 2’s 3’s and 4’s? 1993.
~ Just as the title explains this particular book is good at getting kids familiar with everything that comes in 2’s, 3’s and 4’s. One thing I really like about this book is it uses examples that the children are familiar with, that way it helps them to remember these numbers better.
? 1.02Rote count by 1's, 5's and 10's to 100; by 2's to 20.
? 1.03 Make sets and match numerals up to 30
? 1.08Group and count objects by 2's, 5's, and 10's.

Carlstrom, Nancy. Degen, Bruce; illus. Let’s Count it Out, Jesse Bear. 1998.
~ This book  could be used when trying to teach children numbers 1-20. With each of the numbers 1-10, the author uses a variety of different ideas to portray each number. He chose to represent 11-20 only by having one big picture to go along with each number.
? 1.01Count using one-to-one correspondence to 30.
? 1.06Read number words zero to ten.
? 1.11 Represent numbers in a variety of ways:

Fleming, Denise. Count. 1995.
~ This is a good resource you  might want to use if you want to teach your students about numbers and different animals at the same time. The author of this book has used different animals to portray numbers one through ten. It then goes into counting by 10’s on up to 50 using the same technique.
? 1.01Count using one-to-one correspondence to 30.
? 1.02Rote count by 1's, 5's and 10's to 100; by 2's to 20.
? 1.06Read number words zero to ten.
? 1.08Group and count objects by 2's, 5's, and 10's.
? 1.11 Represent numbers in a variety of ways
? 1.13 Group objects into tens and ones, recognize models; record.

Grover, Max. Amazing and Incredible Counting Stories.1995.
~ This is a really good resource book to use when teaching children their numbers. This particular book goes through number by number from 1-25, then it skips to 50 and begins to introduce counting by 25’s.
? 1.01Count using one-to-one correspondence to 30.
? 1.02Rote count by 1's, 5's and 10's to 100; by 2's to 20.
? 1.05Read and write numerals to 100.
? 1.06Read number words zero to ten.
? 1.08Group and count objects by 2's, 5's, and 10's.
 

McGrath, Barbara. The M&M’s Brand Chocolate Candies Counting Book. 1994.
~ This book is very relative to the kids by using M&M’s; There are many different visuals for each number . Counting goes from #’s 1-12 and dividing 12 into different groups of 2, 3, 4, 5, 6 and uses 6 colors of M&M’s. Shapes are used in this book, allowing the children to learn the sets well if using real M&M’s.
? 1.01Count using one-to-one correspondence to 30.
? 1.02Rote count by 1's, 5's and 10's to 100; by 2's to 20.
? 1.06Read number words zero to ten.
? 1.08Group and count objects by 2's, 5's, and 10's
? 1.11 Represent numbers in a variety of ways
? 1.16 Model the division of sets into two, three or four equal parts;
         explain solution.
 

Second
Adler, David. Tobin, Nancy; Illus. Fraction Fun. 1996.
~ This is a very descriptive book that has to do with fractions, graphing, weighing, and counting. This  books focuses on items that children are familiar with in life, money pizza and fruit, and includes all you need to know about fractions.
? 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
? 1.04 Read word names for numbers to 100.
? 1.05 Use counting strategies such as skip counting by 2's, 5's, and 10's and grouping objects by
               3's and 4's.
? 1.06 Identify odd and even numbers using objects.
? 1.07 Group objects into ones, tens, and hundreds and record in standard form.
? 1.08 Model 3-digit numbers; identify, read, and write correct numerals.

Giganti, Paul. Crews, Donald; illus. Each Orange Has 8 Slices: A Counting Book. 1992
~ This book gives a scenario and then asks several questions about that scenario to help the students understand the concepts a little better. This book covers, addition, subtraction, multiplication, and division.
? 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
? 1.04 Read word names for numbers to 100.
? 1.05 Use counting strategies such as skip counting by 2's, 5's, and 10's and grouping objects by
               3's and 4's.
? 1.06 Identify odd and even numbers using objects.
? 1.07 Group objects into ones, tens, and hundreds and record in standard form.
? 1.08 Model 3-digit numbers; identify, read, and write correct numerals.

Hutchings, Amy & Richard. The Gummy Candy Counting Book. 1997.
This books uses gummy candy to learn to count to 12, and divide 12 into groups of 2, 3, and 4. Each number is accompanied by a poem that is fun, especially for children because they get to use the gummy candy.
? 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
? 1.04 Read word names for numbers to 100.
? 1.05 Use counting strategies such as skip counting by 2's, 5's, and 10's and grouping objects by
               3's and 4's.
? 1.06 Identify odd and even numbers using objects.
? 1.07 Group objects into ones, tens, and hundreds and record in standard form.
? 1.08 Model 3-digit numbers; identify, read, and write correct numerals.

 McGrath, Barbara. The M&M’s Brand Chocolate Candies Counting Book. 1994.
~ This book is very relative to the kids by using M&M’s; There are many different visuals for each number . Counting goes from #’s 1-12 and dividing 12 into different groups of 2, 3, 4, 5, 6 and uses 6 colors of M&M’s. Shapes are used in this book, allowing the children to learn the sets well if using real M&M’s.
? 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
? 1.04 Read word names for numbers to 100.
? 1.05 Use counting strategies such as skip counting by 2's, 5's, and 10's and grouping objects by
               3's and 4's.
? 1.06 Identify odd and even numbers using objects.
? 1.07 Group objects into ones, tens, and hundreds and record in standard form.
? 1.08 Model 3-digit numbers; identify, read, and write correct numerals.

McMillan, Bruce. Jelly Beans For Sale. 1996.
 ~ This is a great book to use to help introduce the concept of money. The way this book goes,
about reaching a sense of money is by comparing it to jelly beans which small children could probably relate to better. This book introduces penny, nickel, dime and quarter.
? 1.03 Compare and order numbers; identify missing numbers in a sequence to 100.
? 1.04 Read word names for numbers to 100.
? 1.06 Identify odd and even numbers using objects.
? 1.07 Group objects into ones, tens, and hundreds and record in standard form.

Third
Hoban, Tana. 26 Letters and 99 Cents. 1996
~ This is a very good resource book for teachers to use in their classroom when teaching students their alphabet and how to count using money. The author chooses to introduce both of the concepts by dividing the book up into two separate books, with one half being money and the other half their letters.
? 1.01 Read and write word names for numbers to 1,000.
? 1.02 Relate standard and expanded notation to 3- and 4-digit numbers.
? 1.03 Compare and order numbers less than 10,000.

Hutchins, Pat. The Doorbell Rang. 1996
This is a good resource book to use when trying to introduce division to young children .The author tries using something children are familiar with in order to teach division by giving a real life example as with homemade cookies. The children have to decide how to go about dividing the cookies up and everytime the doorbell rings a couple more people show up therefore they keep having to divide the cookies up even more.
? 1.06 Model fractions and mixed numbers using regions and sets; describe relationships of parts
? to whole; record.
? 1.07 Compare and order fractions using models; describe comparisons.
? 1.08 Model equivalent fractions using manipulatives and pictures.

McMillan, Bruce.  Eating Fractions. 1978.
~ This is a really good book to use with small children when trying to explain fractions. The author illustrates this idea by using different types of foods to represent fractions. I think that by doing fractions this way it helps children to relate fractions to different things in our everyday life.
? 1.06 Model fractions and mixed numbers using regions and sets; describe relationships of parts
? to whole; record.
? 1.07 Compare and order fractions using models; describe comparisons.
? 1.08 Model equivalent fractions using manipulatives and pictures.

Murphy, Stuart. O’Malley, Kevin; illus. Jump, Kangaroo, Jump. 1999.
~ This book deals with fractions by doing such things as dividing a team into two equal teams for tug of war. It splits a group into thirds for a swimming relay, and into groups of four for a canoe race. This book begins with a stating number of 12 people in the group and then tells you what ½, 1/3,  and ¼ of 12 is. This book also has visual representations of each team.
? 1.06 Model fractions and mixed numbers using regions and sets; describe relationships of parts
? to whole; record.
? 1.07 Compare and order fractions using models; describe comparisons.
? 1.08 Model equivalent fractions using manipulatives and pictures.

Pinczes, Elinor. Mackain, Bonnie; illus. One Hundred Hungry Ants. 1998.
This is a great book to use when trying to help students understand the principles of division. The book is basically about a group of 100 ants that are trying to get to a picnic so they’re trying to decide on how to divide the group up so they can get there quicker.
? 1.06 Model fractions and mixed numbers using regions and sets; describe relationships of parts
? to whole; record.
? 1.07 Compare and order fractions using models; describe comparisons.
? 1.08 Model equivalent fractions using manipulatives and pictures.

Fourth:
McKissack, Patricia. Schutter, Dena; illus. A Million Fish….More Or Less. 1992.
~ A little boy is out on the Bayou fishing, all by himself. To bring excitement in to this book, The little boy has all forms of run-ins with animals such as alligators, raccoons, bears, and snakes., who begins to eat all the million fish that he has caught. The boy begins the day by catching three fish and soon his mind wonders and has him thinking he has caught one million. This book fall under the tall tale and fantasy genre.
? 1.02 Use estimation techniques in determining solutions to problems.
 

Mahy, Margaret. Macarthy, Patricia; illus. 17  Kings and 42 Elephants. 1987.
~ This book deals with multiplication, division, and patterns, that is written as a nonsense poem. It’s a royal romp through the jungle with 17 Kings and 42 elephants as they encounter tigers, crocodiles, peacocks and pelicans along the way. Where all the Kings and elephants are heading is a mystery.
? 1.04 Model, identify, and compare rational numbers (fractions and mixed numbers).
? 1.09 Find the fractional part of a whole number using models and pictures.
? 1.14 Estimate solutions to problems.
? 1.16 Divide using single-digit divisors, with and without remainders.

Hutchins, Pat. The Doorbell Rang. 1996
~ This is a good resource book to use when trying to introduce division to young children .The author tries using something children are familiar with in order to teach division by giving a real life example as with homemade cookies. The children have to decide how to go about dividing the cookies up and everytime the doorbell rings a couple more people show up therefore they keep having to divide the cookies up even more. Lower reading Level.
? 1.02 Use estimation techniques in determining solutions to problems
? 1.04 Model, identify, and compare rational numbers (fractions and mixed numbers).
? 1.14 Estimate solutions to problems.
? 1.16 Divide using single-digit divisors, with and without remainders.
 

Pinczes, Elinor. Mackain, Bonnie; illus. One Hundred Hungry Ants. 1998.
~ This is a great book to use when trying to help students understand the principles of division. The book is basically about a group of 100 ants that are trying to get to a picnic so they’re trying to decide on how to divide the group up so they can get there quicker.
? 1.02 Use estimation techniques in determining solutions to problems
? 1.04 Model, identify, and compare rational numbers (fractions and mixed numbers).
? 1.11 Memorize the division facts related to the multiplication facts/tables through 10.
? 1.16 Divide using single-digit divisors, with and without remainders.
 

Pinczes, Elinor. Mackain, Bonnie; illus. Remainder of One. 1995.
~ This book introduces children to the concept of remainders, through division. The plot of the book is about an Ant named Joe who wants so badly to march in the parade. There are 25 ants, and the lines are always uneven, so he is bumped to make the lines even. Joe is determined that he will march in the parade and begins to work on the problem, rearranging the 25 bugs into separate lines until he is paired up with someone.
? 1.02 Use estimation techniques in determining solutions to problems
? 1.04 Model, identify, and compare rational numbers (fractions and mixed numbers).
? 1.11 Memorize the division facts related to the multiplication facts/tables through 10.
? 1.16 Divide using single-digit divisors, with and without remainders.

Fifth
Shwartz, David M. If you Made a Million. 1989.
~ This is a great book to demonstrate the purpose of money to kids. It introduces the concepts of banks and interest, and talks about different combinations of making the same amount. The illustrations provide great visual examples.
? 1.01 Use place value through millions in real-world situations including reading, writing,
       estimating, and comparing numbers in a variety of forms.
? 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
? 1.15 Estimate results and compute sums and differences with decimal numbers.
? 1.16 Use models and pictures to multiply a whole number by a decimal number; record and
? explain.

Ga’g, Wanda. Millions of Cats. 1956.
~ This is a great book to introduce numbers beyond hundreds. The story and illustrations are entertaining. It is also a good way to begin talking about higher #’s.
? 1.01 Use place value through millions in real-world situations including reading, writing,
       estimating, and comparing numbers in a variety of forms.
? 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
? 1.08 Identify prime and composite numbers less than 100.
? 1.09 Identify equivalent decimals and fractions at the symbolic level. Explain the equivalence.
? 1.10 Compare and order numbers with decimals to the thousandths place; explain solution.

Anno, Mitsumasa. Anno’s Mysterious Multiplying Jars. 1982.
~ This book introduces difficult math concepts in a simple way. Through a creative story and brilliant illustrations, the author creates a mysterious multiplying world inside a jar.
? 1.01 Use place value through millions in real-world situations including reading, writing,
       estimating, and comparing numbers in a variety of forms.
? 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
? 1.08 Identify prime and composite numbers less than 100.
? 1.09 Identify equivalent decimals and fractions at the symbolic level. Explain the equivalence.
? 1.10 Compare and order numbers with decimals to the thousandths place; explain solution.

 Estes, Eleanor. The Hundred Dresses.1972.
~ This Newberry Award winning book is about a young girl from a low income family. While all the other girls are getting new dresses, she was drawing them. This teaches a great lesson about understanding and sympathy towards others and it is also a great way to introduce the concept of one hundred.
? 1.01 Use place value through millions in real-world situations including reading, writing,
       estimating, and comparing numbers in a variety of forms.
? 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
? 1.08 Identify prime and composite numbers less than 100.
? 1.09 Identify equivalent decimals and fractions at the symbolic level. Explain the equivalence.
? 1.10 Compare and order numbers with decimals to the thousandths place; explain solution.

Mathis, Sharon. The Hundred Penny Box. 1975.
~ This is a touching story about a 100 year old woman, and the pennies that represent her life. This book gives meaning to numbers and introduces the concept of one hundred.
? 1.01 Use place value through millions in real-world situations including reading, writing,
       estimating, and comparing numbers in a variety of forms.
? 1.02 Estimate products; multiply any whole number by a 2- or 3-digit factor.
? 1.08 Identify prime and composite numbers less than 100.
? 1.09 Identify equivalent decimals and fractions at the symbolic level. Explain the equivalence.
? 1.10 Compare and order numbers with decimals to the thousandths place; explain solution.

Sixth

Dennis, Richard. Fractions are Parts of Things. 1971.
~ This book takes fractions in the simplest form and builds from there. Using vibrant illustrations of familiar objects, this makes a difficult topic easy, fun and comfortable.
? 1.02 Relate fractions, decimals, and percents.
? 1.03 Compare and order fractions, decimals, and percents.
? 1.04 Multiply and divide fractions, mixed numbers, and decimals using models and pictures;
               record solution.
? 1.05 Multiply and divide fractions, mixed numbers, and decimals.
? 1.06 Add and subtract fractions and mixed numbers with unlike denominators

Simon, Leonard. The Day the Numbers Dissappeared. 1963.
~ This is a cute story to get kids to think about numbers in a different way. The book includes really cute illustrations showing kids having fun with math.

? 1.13 Translate word problems into number sentences and solve. Explain solutions.
? 1.14 Analyze problem situations, determine if there is sufficient information to solve the problem, identify missing or extraneous data, select appropriate strategies, and use an organized approach to solve multi-step problems; use calculators when appropriate.

Hulme, Joy. Sea Sums. 1996.
~ This is a good book to demonstrate to students that math  is everywhere. It’s also a great theme book. It’s basic concepts combined with interesting sea-life vocabulary make for a fun, easy read.
? 1.02 Relate fractions, decimals, and percents.
? 1.03 Compare and order fractions, decimals, and percents.
? 1.04 Multiply and divide fractions, mixed numbers, and decimals using models and pictures;
               record solution.
? 1.05 Multiply and divide fractions, mixed numbers, and decimals.
? 1.06 Add and subtract fractions and mixed numbers with unlike denominators

Adler, David. Tobin, Nancy; Illus. Fraction Fun. 1996.
~ This is a very descriptive book that has to do with fractions, graphing, weighing, and counting. This  books focuses on items that children are familiar with in life, money pizza and fruit, and includes all you need to know about fractions.
? 1.13 Translate word problems into number sentences and solve. Explain solutions.
? 1.14 Analyze problem situations, determine if there is sufficient information to solve the problem, identify missing or extraneous data, select appropriate strategies, and use an organized approach to solve multi-step problems; use calculators when appropriate.

Schwartz, David. If you Hopped Like a Frog.1999.
~ This is a very fun book to use to get kids excited about math. It encourages them to think about math and apply it to themselves and things around them. The illustrations are great and really spark the imagination. It includes concepts like measurement, fractions and large numbers.
? 1.02 Relate fractions, decimals, and percents.
? 1.03 Compare and order fractions, decimals, and percents.
? 1.04 Multiply and divide fractions, mixed numbers, and decimals using models and pictures;
               record solution.
? 1.05 Multiply and divide fractions, mixed numbers, and decimals.
? 1.06 Add and subtract fractions and mixed numbers with unlike denominators
 

Textbook Analysis Of Fractions

K—To explore equal and unequal parts

Charles, Randall, et al. MATH,Vol 2.  Scott Foresman-Addison Wesley, California.1999.

Fractions: Called sharing instead of fractions
? dividing a whole into equal parts
? worksheets that have images of food and dividing it into equal parts.
? Factions are relative to childrens’ lives.

Section b: Sharing
Lesson 1: Equal Parts—Discuss sharing and fair share
Lesson 2: Identify Halves—Separate a shape into 2 equal parts
Lesson 3: Make equal groups—Separate a group of objects into 2 equal parts; review sharing and fair share
Lesson 4: Solve problems by drawing a picture ( review groups up to 10)
 

First—To model and identify equal and unequal parts, halves, 1/4ths and thirds.

Charles, Randall, et al. MATH,Vol 2.  Scott Foresman-Addison Wesley, California.1999.

Chapter 5
Lesson 7: Explore fair shares--Everybody receives the same amount
Lesson 8: Halves—finding pictures that show ½ from a set of pictures and discuss you can tell two equal halves
                coloring activities.
Lesson 9: Fourths—discussion of fourths, finding shapes with 4ths, finding things with four equal parts, coloring
                and creating parts.
Lesson 10: Thirds—same as halves and fourths~ looking at pictures and estimating the fraction.
Lesson 11: Fractions of a set—using unifix cubes to explore fractions
Lesson 12: Probability—shows a picture and tells you to pick out something that may or may not be there. You have to answer whether it is certain you could do the task or impossible.
Lesson 13: Problem Solving—show pictures, ask the students the questions about which one shows 1/3, ½, and ¼

Second—to identify equal parts, halves, fourths, thirds and sixths.

Charles, Randall, et al. MATH,Vol 2.  Scott Foresman-Addison Wesley, California.1999.

Chapter 12 Geometry and Fractions
Section A: Solids and Shapes
Section B: Fractions
 Equal and Unequal
 Unit Fractions
 Fractions
 Estimate Parts of A whole
 Explore a Fraction of a Set

Third—To model fractions as parts of a whole group; to model equivalent fractions and compare fractions; to count parts to make a whole.

Charles, Randall, et al. MATH,Vol 2.  Scott Foresman-Addison Wesley, California.1999.

Chapter 10: Fractions and Customary Linear Measurement
Section A: Understanding Fractions
 Exploring Equal Parts
 Naming and Writing Fractions
 Exploring Equivalent Fractions
 Exploring Comparing and Ordering Fractions
 Estimating Fractional Amounts
Section B: Extending Fraction Concepts
 Fractions and Sets
 Exploring finding a fraction of a number
 Mixed numbers
 Exploring Adding and Subtracting Fractions
Section C: Customary Linear Measurement
 Exploring Length
 Measuring to the nearest ½ inch and ¼ inch
 Exploring length in feet and inches
 Feet, yards, and Miles

Fourth—To use fractions as parts of a whole and a group; to model equivalent fractions using a fraction bar; and to compare and order fractions; to use mixed numbers, and order fractions with like denominators

Charles, Randall et al.. Math Advantage, v.2 Harcourt Brace, Orlando.1999.

Lesson 1: Part of a Whole—to use fractions to represent part of a whole and to read and write fractions
Lesson 2: Part of a group—to use fractions to represent part of a group and to read and write fractions.
Lesson 3: Equivalent Fractions—to investigate equivalent fractions
Lesson 4: Comparing and Ordering Fractions—to compare and order fractions
Lesson 5: Mixed #’s – To identify, red, and write mixed numbers and to rename fractions greater than one as a mixed number.

Fifth—To read and write fractions and find equivalent fractions from models; to compare and order fractions,; to model mixed numbers.

Charles, Randall et al.. Math Advantage, v.2 Harcourt Brace, Orlando.1999.
 
 

Chap 15. Fraction Time with Tangrams
Lesson 1: understanding Fractions—identify, read and write fractions
Lesson 2: mixed Numbers—rename fractions as mixed numbers
Lesson 3: Multiples and Least Common Multiples—to find the LCM of two numbers
Lesson 4: Comparing—To compare fractions with unlike dominators
Lesson 5: Ordering—to order fractions with unlike denominators

Chap 16: Fractions of a number theory
Lesson 3: Equivalent fractions
Lesson 4: Simplest form—to use fraction bars to find an equivalent fraction in a simplest form.
Lesson 5: More about simplest form

Chap 17: Modeling additions of Fractions
Lesson 1: Adding Like Fractions—same denominators
Lesson 2: Adding Unlike Fractions—unlike denominators
Lesson 3: Using the Least Common Denominator to Add Fractions
Lesson 4: Adding Three fractions

Chapter 18: Modeling Subtractions of Fractions
Lesson 1: Subtracting Like Fractions
Lesson 2: Subtracting Unlike fractions
Lesson 3: Using the LCD to subtract fractions
Lesson 4: Subtracting fractions using a ruler

Chapter 19: Adding and Subtracting Fractions
Lesson 1: Estimating sums and differences
Lesson 2: Adding and subtracting like fractions
Lesson 3: Adding and subtracting unlike fractions

Chapter 20: Adding and Subtracting Mixed Numbers
Lesson 1: Estimating sums and differences
Lesson 2: Adding mixed numbers
Lesson 3: Subtracting mixed numbers

Chapter 22: Multiplying Fractions
Lesson 1: Multiplying fractions and whole numbers
Lesson 2: multiplying a fraction by a fraction
Lesson 3: multiplying fractions and mixed numbers

Sixth—To write fractions in simplest form, to write fractions as mixed numbers, and mixed numbers as fractions; to find LCM and GCF.

Charles, Randall et al..Math Advantage, v.2 Harcourt Brace, Orlando.1999.

Chapter 1: Looking at numbers
Lesson 3: Decimals and Fractions

Chapter 4: Number theory and Fractions
Lesson 4: Fractions in simplest form
Lesson 5: mixed numbers and fractions

Chapter 5: Adding and subtracting fractions
Lesson 1: adding and subtracting like fractions
Lesson 2: adding and subtracting unlike fractions
Lesson 3: adding unlike fractions
Lesson 4: subtracting unlike fractions

Chapter 6: Adding and Subtracting Mixed numbers
Lesson 1: adding mixed numbers
Lesson 2: subtracting mixed numbers
Lesson 3: adding and subtracting mixed numbers
Lesson 4: estimating sums and differences

Chapter 7: Multiplying and dividing fractions
Lesson 1: Multiplying with fractions
Lesson 2: simplifying fractions
Lesson 3: mixed numbers
Lesson 4: dividing fractions

What is so Difficult?

K—relating numbers to real objects, place value---hard to grasp that you use the same 10 digits to make all numbers

1—subtraction

2—subtraction with regrouping

3—fractions/decimals--- have extreme trouble in visualizing parts of wholes.

4—fractions/decimals---have extreme trouble in visualizing parts of wholes.

5—Fractions---(adding, subtracting, multiplying, dividing)

6—fractions—multiplying and dividing fractions
 
 
 
 

BY: Jenifer F.
      Lisa M.
      Christi W.
      Abby M.
 
 

    For my math lesson plan, I chose to teach about place value under Numeration. I remember when I was in school that this was a critical part of math, and for a lot of children it was a difficult concept For my lesson plan, we used a place value chart as a manipulative as well as a bulls-eye game board, and a book. For Place Value it was a little difficult to locate many manipulatives, so I decided to use a lesson that would refresh us on place value, and then play a game that would aid in their comprehension.
     As for a resource, I began by reading the book How Much Is A Million? As we read this book, we focused on the concepts of million, billion, and trillion. The Magician takes the reader on a journey to explain these concepts. Through this book, I feel that children can gain a better understanding of these large numbers. The concept of this book was on Place Value, and it helps children to grasp these concepts due to the detailed illustration and descriptions.
     Before reading the book, I asked the students about their understanding of place value. Have the students brainstorm times and places that they may encounter these large numbers. After reading the book, I would give the students a place value chart and have them write out numbers such as one million, two hundred thousand, and six million. I would also have them take a number and write it out numerically. After this occurs, the students would be partnered off and discuss their answers. Once their answers have been discussed, we would begin playing our game. The game is called Bulls-eye, and would be labeled as follows: inside circle, millions; next circle thousands; next circle hundreds; next circle tens and last circle ones. Each pair of students would be given twenty-five paper clips and would have to pitch the paper clips at the bulls-eye and figure out their score by adding up the numbers. They will use expanded notion first and then write out the number. If the students have difficulty adding the numbers, I would have them use their place value charts. The pair with the largest number wins.
     I am not real sure if this lesson would pass as a manipulative or a resource, but I felt that the book would. The mathematics represented by the bulls-eye is great for learning addition as well as subtraction if you wanted to use it that way. The place value chart is used to represent place value. I learned that this is actually a great form of assessment for the classroom, and enables me to find out where students are in their understanding. It allows me to know if the children are ready to move on or not.