Fall 2010 1 K – 2 VDOE Mathematics Institute 2010 K – 2 VDOE Mathematics Institute 2010.

Fall 2010

1

K – 2 VDOE Mathematics Institute

2010

K – 2 VDOE Mathematics Institute

2010

Fall 2010

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Purpose and Goals Purpose and Goals Purpose and Goals Purpose and Goals

• Support implementation of the 2009 Standards

• Understand Vertical Progression for K-2 SOL

• Identify Challenging SOL and how to address them

• Highlight effective teaching practices in mathematics

• Focus on Number and Number Sense while highlighting other strands and connections between them

• Support implementation of the 2009 Standards

• Understand Vertical Progression for K-2 SOL

• Identify Challenging SOL and how to address them

• Highlight effective teaching practices in mathematics

• Focus on Number and Number Sense while highlighting other strands and connections between them

Fall 2010

Unpacking Number Unpacking Number and and

Number SenseNumber Sense

Unpacking Number Unpacking Number and and

Number SenseNumber Sense

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Fall 2010

Number and Number SenseNumber and Number SenseKindergartenKindergarten

Number and Number SenseNumber and Number SenseKindergartenKindergarten

K.1 The student, given two sets containing 10 or fewer concrete items, will K.1 The student, given two sets containing 10 or fewer concrete items, will

identify and describe one set as having more, fewer, or the same number of identify and describe one set as having more, fewer, or the same number of

members as the other set, using the concept of one - to - one members as the other set, using the concept of one - to - one

correspondence.correspondence.

K.2 The student, given a set containing 10 or fewer concrete items, willK.2 The student, given a set containing 10 or fewer concrete items, will

a) tell how many are in the set by counting the number of items orally;a) tell how many are in the set by counting the number of items orally;

b) select the corresponding numeral from a given set; andb) select the corresponding numeral from a given set; and

c) write the numeral to tell how many are in the set.c) write the numeral to tell how many are in the set.

K.3 The student, given an ordered set of three objects and/or pictures, will K.3 The student, given an ordered set of three objects and/or pictures, will

indicate the ordinal position of each item, first through third, and the ordered indicate the ordinal position of each item, first through third, and the ordered

position of each item from left-to-right, right-to- left, top-to-bottom, and/or position of each item from left-to-right, right-to- left, top-to-bottom, and/or

bottom- to-top.bottom- to-top.

K.4 The student will investigate and recognize patterns from counting by fives K.4 The student will investigate and recognize patterns from counting by fives

and tens to 30,using concrete objects and a calculator.and tens to 30,using concrete objects and a calculator.

K.5 The student will count forward to 30 and backward from 10.K.5 The student will count forward to 30 and backward from 10.

K.1 The student, given two sets containing 10 or fewer concrete items, will K.1 The student, given two sets containing 10 or fewer concrete items, will

identify and describe one set as having more, fewer, or the same number of identify and describe one set as having more, fewer, or the same number of

members as the other set, using the concept of one - to - one members as the other set, using the concept of one - to - one

correspondence.correspondence.

K.2 The student, given a set containing 10 or fewer concrete items, willK.2 The student, given a set containing 10 or fewer concrete items, will

a) tell how many are in the set by counting the number of items orally;a) tell how many are in the set by counting the number of items orally;

b) select the corresponding numeral from a given set; andb) select the corresponding numeral from a given set; and

c) write the numeral to tell how many are in the set.c) write the numeral to tell how many are in the set.

K.3 The student, given an ordered set of three objects and/or pictures, will K.3 The student, given an ordered set of three objects and/or pictures, will

indicate the ordinal position of each item, first through third, and the ordered indicate the ordinal position of each item, first through third, and the ordered

position of each item from left-to-right, right-to- left, top-to-bottom, and/or position of each item from left-to-right, right-to- left, top-to-bottom, and/or

bottom- to-top.bottom- to-top.

K.4 The student will investigate and recognize patterns from counting by fives K.4 The student will investigate and recognize patterns from counting by fives

and tens to 30,using concrete objects and a calculator.and tens to 30,using concrete objects and a calculator.

K.5 The student will count forward to 30 and backward from 10.K.5 The student will count forward to 30 and backward from 10. 4

Fall 2010

Number and Number SenseNumber and Number SenseGrade 1Grade 1


5

1.1 The student will count objects in a given set containing between 1 and 100 1.1 The student will count objects in a given set containing between 1 and 100

objects and write the corresponding numeral.objects and write the corresponding numeral.

1.2 The student will group a collection of up to 100 objects into tens and ones 1.2 The student will group a collection of up to 100 objects into tens and ones

and write the corresponding numeral to develop an understanding of place and write the corresponding numeral to develop an understanding of place

value.value.

1.3 The student will count forward by ones, fives, and tens to 100, by twos to 1.3 The student will count forward by ones, fives, and tens to 100, by twos to

20, and backward by ones from 20.20, and backward by ones from 20.

1.4 The student will recognize and write numerals 0 through 100.1.4 The student will recognize and write numerals 0 through 100.

1.5 The student will identify the ordinal positions first through tenth, using an 1.5 The student will identify the ordinal positions first through tenth, using an

ordered set of objects.ordered set of objects.

1.6 The student will identify and represent the concepts of one-half and one- 1.6 The student will identify and represent the concepts of one-half and one-

fourth, using appropriate materials or a drawing.fourth, using appropriate materials or a drawing.

1.1 The student will count objects in a given set containing between 1 and 100 1.1 The student will count objects in a given set containing between 1 and 100

objects and write the corresponding numeral.objects and write the corresponding numeral.

1.2 The student will group a collection of up to 100 objects into tens and ones 1.2 The student will group a collection of up to 100 objects into tens and ones

and write the corresponding numeral to develop an understanding of place and write the corresponding numeral to develop an understanding of place

value.value.

1.3 The student will count forward by ones, fives, and tens to 100, by twos to 1.3 The student will count forward by ones, fives, and tens to 100, by twos to

20, and backward by ones from 20.20, and backward by ones from 20.

1.4 The student will recognize and write numerals 0 through 100.1.4 The student will recognize and write numerals 0 through 100.

1.5 The student will identify the ordinal positions first through tenth, using an 1.5 The student will identify the ordinal positions first through tenth, using an

ordered set of objects.ordered set of objects.

1.6 The student will identify and represent the concepts of one-half and one- 1.6 The student will identify and represent the concepts of one-half and one-

fourth, using appropriate materials or a drawing.fourth, using appropriate materials or a drawing.

Fall 2010



2.1 The student will2.1 The student will

a)a) read, write, and identify the place value of each digit in a three-digit numeral, using read, write, and identify the place value of each digit in a three-digit numeral, using

numeration models; andnumeration models; and

b) round two-digit numbers to the nearest ten.b) round two-digit numbers to the nearest ten.

2.2 The student will compare two whole numbers between 0 and 999, using symbols2.2 The student will compare two whole numbers between 0 and 999, using symbols

(>, <, or =) and words ((>, <, or =) and words (greater than, less than, or equal to).greater than, less than, or equal to).

2.3 The student will identify the ordinal positions first through twentieth, using an 2.3 The student will identify the ordinal positions first through twentieth, using an

ordered setordered set

of objectsof objects

2.4 The student will identify the part of a set and/or region that represents fractions for one-half,2.4 The student will identify the part of a set and/or region that represents fractions for one-half,

one-third, one-fourth, one-eighth, and one-tenth and write the correspondingone-third, one-fourth, one-eighth, and one-tenth and write the corresponding

fraction.fraction.


a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5,a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5,

or 10, using mental mathematics, paper and pencil, hundred chart, calculators,or 10, using mental mathematics, paper and pencil, hundred chart, calculators,

and/or concrete objects, as appropriate;and/or concrete objects, as appropriate;

b) count backward by tens from 100;b) count backward by tens from 100;

c) group objects by threes and fours; andc) group objects by threes and fours; and

d) recognize even and odd numbers, using objects.d) recognize even and odd numbers, using objects.


a)a) read, write, and identify the place value of each digit in a three-digit numeral, using read, write, and identify the place value of each digit in a three-digit numeral, using

numeration models; andnumeration models; and

b) round two-digit numbers to the nearest ten.b) round two-digit numbers to the nearest ten.

2.2 The student will compare two whole numbers between 0 and 999, using symbols2.2 The student will compare two whole numbers between 0 and 999, using symbols

(>, <, or =) and words ((>, <, or =) and words (greater than, less than, or equal to).greater than, less than, or equal to).

2.3 The student will identify the ordinal positions first through twentieth, using an 2.3 The student will identify the ordinal positions first through twentieth, using an

ordered setordered set

of objectsof objects

2.4 The student will identify the part of a set and/or region that represents fractions for one-half,2.4 The student will identify the part of a set and/or region that represents fractions for one-half,

one-third, one-fourth, one-eighth, and one-tenth and write the correspondingone-third, one-fourth, one-eighth, and one-tenth and write the corresponding

fraction.fraction.


a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5,a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5,

or 10, using mental mathematics, paper and pencil, hundred chart, calculators,or 10, using mental mathematics, paper and pencil, hundred chart, calculators,

and/or concrete objects, as appropriate;and/or concrete objects, as appropriate;

b) count backward by tens from 100;b) count backward by tens from 100;

c) group objects by threes and fours; andc) group objects by threes and fours; and

d) recognize even and odd numbers, using objects.d) recognize even and odd numbers, using objects. 6

Fall 2010

Standard: Standard: Standard: Standard:

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Number and Number Sense

What do students have to do? Look for verbs.

With what? With what parameters? Which figures, numbers, shapes?

Vocabulary Essential Understandings

Fall 2010

Number and Number SenseNumber and Number SenseNumber and Number SenseNumber and Number SenseK.2 The student, given a set K.2 The student, given a set containing 15 or fewer containing 15 or fewer concrete objects, will concrete objects, will

a)a)tell how many are in the tell how many are in the set by counting the number set by counting the number of objects orally;of objects orally;

b)b)write the numeral to tell write the numeral to tell how many are in the set; andhow many are in the set; and

c)c)select the corresponding select the corresponding numeral from a given set of numeral from a given set of numerals.numerals.

K.2 The student, given a set K.2 The student, given a set containing 15 or fewer containing 15 or fewer concrete objects, will concrete objects, will

a)a)tell how many are in the tell how many are in the set by counting the number set by counting the number of objects orally;of objects orally;

b)b)write the numeral to tell write the numeral to tell how many are in the set; andhow many are in the set; and

c)c)select the corresponding select the corresponding numeral from a given set of numeral from a given set of numerals.numerals.

•Same, Less, More•One More/ One Less•Garbage •Think Board •Equal Schmequal •Roll and Color •Roll and Write

•Same, Less, More•One More/ One Less•Garbage •Think Board •Equal Schmequal •Roll and Color •Roll and Write

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Fall 2010

Number and Number SenseNumber and Number SenseNumber and Number SenseNumber and Number Sense


a) count from 0 to 100 and a) count from 0 to 100 and write the corresponding write the corresponding numerals; andnumerals; and

b) group a collection of up to b) group a collection of up to 100 objects into tens and 100 objects into tens and ones and write the ones and write the corresponding numeral to corresponding numeral to develop an understanding of develop an understanding of place value.place value.


a) count from 0 to 100 and a) count from 0 to 100 and write the corresponding write the corresponding numerals; andnumerals; and

b) group a collection of up to b) group a collection of up to 100 objects into tens and 100 objects into tens and ones and write the ones and write the corresponding numeral to corresponding numeral to develop an understanding of develop an understanding of place value.place value.

•Beaded Number LineBeaded Number Line•Beaded Number LineBeaded Number Line

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Fall 2010

Number and Number SenseNumber and Number SenseNumber and Number SenseNumber and Number Sense

2.1 The student will

b) round two-digit numbers to the nearest ten

2.1 The student will

b) round two-digit numbers to the nearest ten

•Beaded Number LineBeaded Number Line•Beaded Number LineBeaded Number Line

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Fall 2010

Kindergarten, First Grade and Kindergarten, First Grade and Second GradeSecond Grade

Kindergarten, First Grade and Kindergarten, First Grade and Second GradeSecond Grade

NUMBER AND NUMBER SENSE: NUMBER AND NUMBER SENSE:

CONNECTIONS CONNECTIONS

TO OTHERTO OTHER

2009 MATHEMATICS 2009 MATHEMATICS

STRANDSSTRANDS

NUMBER AND NUMBER SENSE: NUMBER AND NUMBER SENSE:

CONNECTIONS CONNECTIONS

TO OTHERTO OTHER

2009 MATHEMATICS 2009 MATHEMATICS

STRANDSSTRANDS

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Fall 2010

Computation and Estimation Computation and Estimation Computation and Estimation Computation and Estimation

Connected to N&NS SOL 2.1Connected to N&NS SOL 2.1

2.6 The student, given two 2.6 The student, given two whole numbers whose sum whole numbers whose sum is 99 or less, willis 99 or less, will

b) find the sum, using b) find the sum, using various methods of various methods of calculation.calculation.

2.7 The student, given two 2.7 The student, given two whole numbers, each of whole numbers, each of which is 99 or less, willwhich is 99 or less, will

b) find the difference, using b) find the difference, using various methods of various methods of calculation.calculation.


2.6 The student, given two 2.6 The student, given two whole numbers whose sum whole numbers whose sum is 99 or less, willis 99 or less, will

b) find the sum, using b) find the sum, using various methods of various methods of calculation.calculation.

2.7 The student, given two 2.7 The student, given two whole numbers, each of whole numbers, each of which is 99 or less, willwhich is 99 or less, will

b) find the difference, using b) find the difference, using various methods of various methods of calculation.calculation.

•Beaded Number LineBeaded Number Line

•Empty Number LineEmpty Number Line

•Beaded Number LineBeaded Number Line

•Empty Number LineEmpty Number Line

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Fall 2010

Number and Number Sense Connections to Number and Number Sense Connections to Computation and Estimation as Computation and Estimation as

Fact Strategies Fact Strategies

Number and Number Sense Connections to Number and Number Sense Connections to Computation and Estimation as Computation and Estimation as

Fact Strategies Fact Strategies Connected to N&NS SOL K.4Connected to N&NS SOL K.4

K.4 The student willK.4 The student will

b) identify one more than a b) identify one more than a number and one less than a number and one less than a numbernumber

C&E:C&E:

1.5 The student will recall 1.5 The student will recall basic addition facts with sums basic addition facts with sums to 18 or less and the to 18 or less and the corresponding subtraction corresponding subtraction facts.facts.

2.5 The student will recall 2.5 The student will recall addition facts with addition facts with sums to 20sums to 20 or less and the corresponding or less and the corresponding subtraction factssubtraction facts

Connected to N&NS SOL K.4Connected to N&NS SOL K.4



C&E:C&E:

1.5 The student will recall 1.5 The student will recall basic addition facts with sums basic addition facts with sums to 18 or less and the to 18 or less and the corresponding subtraction corresponding subtraction facts.facts.


•Build a StackBuild a Stack•Neighbor FactsNeighbor Facts•Quick ImagesQuick Images•Dot CardsDot Cards•Ten FramesTen Frames•GarbageGarbage

•Build a StackBuild a Stack•Neighbor FactsNeighbor Facts•Quick ImagesQuick Images•Dot CardsDot Cards•Ten FramesTen Frames•GarbageGarbage

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Fall 2010

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Fall 2010

Draw ItDraw ItDraw ItDraw It

How Many?How Many?How Many?How Many?

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Fall 2010

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Fall 2010

Draw ItDraw ItDraw ItDraw It

How Many?How Many?How Many?How Many?

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Fall 2010

Fact StrategiesFact StrategiesFact StrategiesFact Strategies




C&E:C&E:

1.5 The student will recall basic 1.5 The student will recall basic addition facts with sums to 18 addition facts with sums to 18 or less and the corresponding or less and the corresponding subtraction facts.subtraction facts.





C&E:C&E:

1.5 The student will recall basic 1.5 The student will recall basic addition facts with sums to 18 addition facts with sums to 18 or less and the corresponding or less and the corresponding subtraction facts.subtraction facts.


• Chop/SnapChop/Snap• Turn over TenTurn over Ten• Tens Go FishTens Go Fish• Double Cover-upDouble Cover-up

• Chop/SnapChop/Snap• Turn over TenTurn over Ten• Tens Go FishTens Go Fish• Double Cover-upDouble Cover-up

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Fall 2010

Inverse RelationshipsInverse RelationshipsInverse RelationshipsInverse RelationshipsConnected to N&NS SOL 2.1, 2.4

C&E:

2.5 The student will recall addition recall addition facts with facts with sums to 20 or less and or less and the corresponding subtraction the corresponding subtraction facts.facts.

2.92.9 The student will recognize The student will recognize andand

describe the related facts thatdescribe the related facts that

represent and describe therepresent and describe the

inverse relationship betweeninverse relationship between

addition and subtraction.addition and subtraction.

Connected to N&NS SOL 2.1, 2.4

C&E:

2.5 The student will recall addition recall addition facts with facts with sums to 20 or less and or less and the corresponding subtraction the corresponding subtraction facts.facts.

2.92.9 The student will recognize The student will recognize andand

describe the related facts thatdescribe the related facts that

represent and describe therepresent and describe the

inverse relationship betweeninverse relationship between

addition and subtraction.addition and subtraction.

•Spill the BeansSpill the Beans•Counters in a CupCounters in a Cup•Bears in a Cave Bears in a Cave

•Spill the BeansSpill the Beans•Counters in a CupCounters in a Cup•Bears in a Cave Bears in a Cave

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Fall 2010

EqualityEqualityEqualityEquality

Connected to N&NS SOL 2.1cConnected to N&NS SOL 2.1c

1.18 The student will demonstrate an 1.18 The student will demonstrate an understanding of equality through the understanding of equality through the use of the equal sign.use of the equal sign.

2.22 The student will demonstrate an 2.22 The student will demonstrate an understanding of equality by understanding of equality by recognizing that the symbol = in an recognizing that the symbol = in an equation indicates equivalent equation indicates equivalent quantities and the symbol ≠ indicates quantities and the symbol ≠ indicates that quantities are not equivalent.that quantities are not equivalent.

Connected to N&NS SOL 2.1cConnected to N&NS SOL 2.1c

1.18 The student will demonstrate an 1.18 The student will demonstrate an understanding of equality through the understanding of equality through the use of the equal sign.use of the equal sign.

2.22 The student will demonstrate an 2.22 The student will demonstrate an understanding of equality by understanding of equality by recognizing that the symbol = in an recognizing that the symbol = in an equation indicates equivalent equation indicates equivalent quantities and the symbol ≠ indicates quantities and the symbol ≠ indicates that quantities are not equivalent.that quantities are not equivalent.

•Circle Maps•Number Balance

Activities•Measurement Model

using cubes

•Circle Maps•Number Balance

Activities•Measurement Model

using cubes

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Fall 2010




b) identify examples of the b) identify examples of the identity and commutative identity and commutative propertiesproperties for addition and for addition and multiplicationmultiplication



b) identify examples of the b) identify examples of the identity and commutative identity and commutative propertiesproperties for addition and for addition and multiplicationmultiplication

Identity Property of Addition

Identity Property of Multiplication

Commutative Property of Addition and Multiplication



Commutative Property of Addition and Multiplication

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Fall 2010



8 + 0 = 8

Commutative Property of Addition

4 + 3 = 3 + 4


8 + 0 = 8

Commutative Property of Addition

4 + 3 = 3 + 4


8 x 1 = 8

Commutative Property of Multiplication

2 x 5 = 5 x 2


8 x 1 = 8

Commutative Property of Multiplication

2 x 5 = 5 x 2

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Fall 2010

is about seeing (interpreting, describing, is about seeing (interpreting, describing, explaining) situations mathematically, explaining) situations mathematically, and not simply about executing rules, and not simply about executing rules, procedures, or skills expertly. Students procedures, or skills expertly. Students need opportunities to solve various need opportunities to solve various problem types through modeling to problem types through modeling to strengthen their mathematics strengthen their mathematics understandings and use of concepts and understandings and use of concepts and skills. skills.

is about seeing (interpreting, describing, is about seeing (interpreting, describing, explaining) situations mathematically, explaining) situations mathematically, and not simply about executing rules, and not simply about executing rules, procedures, or skills expertly. Students procedures, or skills expertly. Students need opportunities to solve various need opportunities to solve various problem types through modeling to problem types through modeling to strengthen their mathematics strengthen their mathematics understandings and use of concepts and understandings and use of concepts and skills. skills.

Problem Solving…Problem Solving…

Fall 2010

Multistep Problem Solving Multistep Problem Solving involves:involves:

Multistep Problem Solving Multistep Problem Solving involves:involves:

• the use of two or morethe use of two or more

operations; andoperations; and

• operations can be different.operations can be different.

• the use of two or morethe use of two or more

operations; andoperations; and

• operations can be different.operations can be different.

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Fall 2010

Example:Example:Example:Example:

Emily is reading the latest Magic Emily is reading the latest Magic

Maggie book. She reads 12 Maggie book. She reads 12

pages each day. After 7 days, pages each day. After 7 days,

Emily still has 20 pages left toEmily still has 20 pages left to

read. How many pages are in read. How many pages are in

Emily's book?Emily's book?

Emily is reading the latest Magic Emily is reading the latest Magic

Maggie book. She reads 12 Maggie book. She reads 12

pages each day. After 7 days, pages each day. After 7 days,

Emily still has 20 pages left toEmily still has 20 pages left to

read. How many pages are in read. How many pages are in

Emily's book?Emily's book?25

Fall 2010

Problem SolvingComputation and Estimation

Problem SolvingComputation and Estimation


1.6 The student will create and solve one-1.6 The student will create and solve one-step story and picture problems using step story and picture problems using basic addition facts with sums 10 18 or basic addition facts with sums 10 18 or less and the corresponding subtraction less and the corresponding subtraction facts. facts.

2.8 The student will create and solve one- 2.8 The student will create and solve one- and two-stepand two-step addition and subtraction addition and subtraction problems, using data from simple tables, problems, using data from simple tables, picture graphs, and bar graphspicture graphs, and bar graphs

3.4 The student will estimate solutions3.4 The student will estimate solutions

to and solve single-step and multistep to and solve single-step and multistep problems involving the sum and difference problems involving the sum and difference of two whole numbers, each 9,999 or less, of two whole numbers, each 9,999 or less, with or without regrouping.with or without regrouping.


1.6 The student will create and solve one-1.6 The student will create and solve one-step story and picture problems using step story and picture problems using basic addition facts with sums 10 18 or basic addition facts with sums 10 18 or less and the corresponding subtraction less and the corresponding subtraction facts. facts.

2.8 The student will create and solve one- 2.8 The student will create and solve one- and two-stepand two-step addition and subtraction addition and subtraction problems, using data from simple tables, problems, using data from simple tables, picture graphs, and bar graphspicture graphs, and bar graphs

3.4 The student will estimate solutions3.4 The student will estimate solutions

to and solve single-step and multistep to and solve single-step and multistep problems involving the sum and difference problems involving the sum and difference of two whole numbers, each 9,999 or less, of two whole numbers, each 9,999 or less, with or without regrouping.with or without regrouping.

•Classify Types of Classify Types of ProblemsProblems

•Create problems Create problems according to typeaccording to type

•Gallery WalkGallery Walk

•Classify Types of Classify Types of ProblemsProblems

•Create problems Create problems according to typeaccording to type

•Gallery WalkGallery Walk

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Fall 2010

Vary the types of problems Vary the types of problems students experience because students experience because they need opportunities to solve they need opportunities to solve various problem types through various problem types through modeling to strengthen their modeling to strengthen their mathematics understandings and mathematics understandings and use of concepts and skills.use of concepts and skills.

Vary the types of problems Vary the types of problems students experience because students experience because they need opportunities to solve they need opportunities to solve various problem types through various problem types through modeling to strengthen their modeling to strengthen their mathematics understandings and mathematics understandings and use of concepts and skills.use of concepts and skills.

Fall 2010

Problem Solving TypesProblem Solving TypesProblem Solving TypesProblem Solving Types

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Fall 2010

Multistep Problem Solving Multistep Problem Solving

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Fall 2010

Multistep Problem Solving Multistep Problem Solving

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•Create a multistep problem

•Share

•Create a multistep problem

•Share

Fall 2010

FractionsFractionsFractionsFractions

K.5 The student will identify the K.5 The student will identify the parts of a set and/or a region parts of a set and/or a region that represent fractions for that represent fractions for halves and fourths.halves and fourths.

K.5 The student will identify the K.5 The student will identify the parts of a set and/or a region parts of a set and/or a region that represent fractions for that represent fractions for halves and fourths.halves and fourths.

•Fraction Circle PlatesFraction Circle Plates•Fraction Circle PlatesFraction Circle Plates

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Fall 2010

FractionsFractionsFractionsFractions1.3 The student will identify the 1.3 The student will identify the parts of a set and/or region that parts of a set and/or region that represent fractions for halves, represent fractions for halves, thirds, and fourths and write the thirds, and fourths and write the fractions.fractions.

2.32.3 The student willThe student will

a)a) identify the parts of a set identify the parts of a set and/or region that represent and/or region that represent fractions for halves, thirds, fourths, fractions for halves, thirds, fourths, sixths, eighths, and tenths;sixths, eighths, and tenths;

b)b) write the fractions; andwrite the fractions; and

c)c) compare the unit fractions compare the unit fractions for halves, thirds, fourths, sixths, for halves, thirds, fourths, sixths, eighths, and tenthseighths, and tenths..

1.3 The student will identify the 1.3 The student will identify the parts of a set and/or region that parts of a set and/or region that represent fractions for halves, represent fractions for halves, thirds, and fourths and write the thirds, and fourths and write the fractions.fractions.

2.32.3 The student willThe student will

a)a) identify the parts of a set identify the parts of a set and/or region that represent and/or region that represent fractions for halves, thirds, fourths, fractions for halves, thirds, fourths, sixths, eighths, and tenths;sixths, eighths, and tenths;

b)b) write the fractions; andwrite the fractions; and

c)c) compare the unit fractions compare the unit fractions for halves, thirds, fourths, sixths, for halves, thirds, fourths, sixths, eighths, and tenthseighths, and tenths..

• Fraction SortFraction Sort• Compare Compare Unit nit

FractionsFractions• Fraction WarFraction War• One Away from One Away from

WholeWhole• Making Making

GeneralizationsGeneralizations

• Fraction SortFraction Sort• Compare Compare Unit nit

FractionsFractions• Fraction WarFraction War• One Away from One Away from

WholeWhole• Making Making

GeneralizationsGeneralizations

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Fall 2010

Process StandardsProcess StandardsProcess StandardsProcess Standards

• Problem SolvingProblem Solving

• CommunicationCommunication

• Reasoning and ProofReasoning and Proof

• RepresentationsRepresentations

• ConnectionsConnections

• Problem SolvingProblem Solving

• CommunicationCommunication

• Reasoning and ProofReasoning and Proof

• RepresentationsRepresentations

• ConnectionsConnections

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Fall 2010

Good QuestioningGood QuestioningGood QuestioningGood Questioning

How did you solve it?How did you solve it? What was your strategy?What was your strategy? How do you know?How do you know? Can you prove that it always works with other Can you prove that it always works with other

numbers?numbers? Does anyone have another strategy?Does anyone have another strategy?

How did you solve it?How did you solve it? What was your strategy?What was your strategy? How do you know?How do you know? Can you prove that it always works with other Can you prove that it always works with other

numbers?numbers? Does anyone have another strategy?Does anyone have another strategy?

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Fall 2010

3 , 2 , 1 …..Then you’ll be done!3 , 2 , 1 …..Then you’ll be done!3 , 2 , 1 …..Then you’ll be done!3 , 2 , 1 …..Then you’ll be done!

ON YOUR EXIT CARD PLEASE WRITE DOWN…..ON YOUR EXIT CARD PLEASE WRITE DOWN…..

3 KEY THINGS YOU’VE LEARNED3 KEY THINGS YOU’VE LEARNED

2 THINGS YOU ARE STILL THINKING ABOUT2 THINGS YOU ARE STILL THINKING ABOUT

1 PLAN OF WHAT WILL BE THE NEXT STEPS1 PLAN OF WHAT WILL BE THE NEXT STEPS

ON YOUR EXIT CARD PLEASE WRITE DOWN…..ON YOUR EXIT CARD PLEASE WRITE DOWN…..

3 KEY THINGS YOU’VE LEARNED3 KEY THINGS YOU’VE LEARNED

2 THINGS YOU ARE STILL THINKING ABOUT2 THINGS YOU ARE STILL THINKING ABOUT

1 PLAN OF WHAT WILL BE THE NEXT STEPS1 PLAN OF WHAT WILL BE THE NEXT STEPS

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Fall 2010

THANKS FOR COMING!THANKS FOR COMING!

Making Mathematics Making Mathematics Meaningful for AllMeaningful for All

THANKS FOR COMING!THANKS FOR COMING!

Making Mathematics Making Mathematics Meaningful for AllMeaningful for All

39

Fall 2010 1 K – 2 VDOE Mathematics Institute 2010 K – 2 VDOE Mathematics Institute 2010.

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Transcript of Fall 2010 1 K – 2 VDOE Mathematics Institute 2010 K – 2 VDOE Mathematics Institute 2010.