incorporating addition & subtraction strategies based on ...€¦ · incorporating addition...

Place ValueWITH

Incorporating Addition & Subtraction Strategies

Based On

CHRISTINA TONDEVOLD

Toy Car TaskDraw a representation of this problem:

There is a bag of toy car wheels. In the bag, there are enough wheels for 6 toy cars with 2 wheels left over. How many wheels are in the bag?

26

Toy Car Task There is a bag of toy car wheels. In

the bag, there are enough wheels for 6 toy cars with 2 wheels left over. How many wheels are in the bag?

Where is the 2 and 6?

https://www.youtube.com/watch?v=_ofQ_WnQiZ4

https://www.youtube.com/watch?v=_ofQ_WnQiZ4

Place ValueHow many tens are in 53? How many tens are in 243? How many tens are in 1,037?

A candy factory had 48,638 candy bars to

put into boxes holding 100 candy

bars each. How many boxes will they need?

Candy Factory

7

http://www.historybyzim.com/2013/01/candy-factory/



A BOLD STATEMENTThis is Another

Grade Standards

K•Solve +/- word problems within 10 using objects or drawings. •Fluently +/- within 5.

1

•Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…

•Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…

2

•Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

•Add up to four two-digit numbers using strategies based on place value and properties of operations.

•Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

3•Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

4 •Fluently add/subtract multi-digit whole numbers using the standard algorithm.

A BOLD STATEMENTThis is Another

Grade Standards

K

•Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

1

•Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

A. 10 can be thought of as a bundle of ten ones — called a “ten.”

B. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

C. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

2

•Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

A. 100 can be thought of as a bundle of ten tens — called a “hundred.” B. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six,

seven, eight, or nine hundreds (and 0 tens and 0 ones).

3

4•Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

Grade Standards

K

•Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

1

•Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

A. 10 can be thought of as a bundle of ten ones — called a “ten.”

B. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

C. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

2

•Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

A. 100 can be thought of as a bundle of ten tens — called a “hundred.”

B. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

3

4

•Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

Grade Standards

K

•Solve +/- word problems within 10 using objects or drawings. •Fluently +/- within 5.

1

•Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…

•Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction…

2

•Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

•Add up to four two-digit numbers using strategies based on place value and properties of operations.

•Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

3

•Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

4 •Fluently add/subtract multi-digit whole numbers using the standard algorithm.

Strategies are Context Based

57-19 66-43100-98

Strategies are Context Based

Sierra has $57. She spends $19 on slime supplies. How much does she

have left?

Sierra has $19. She wants a slime kit that is $57. How much does she need before she has enough to buy the kit?

Mental Math

57-19

Strategies

57 = 50 + 7 - 19 = - 10 - 9 38 = - 240

57 = 50 + 7 - 19 = - 10 - 9

40 17

38 = 30 8

245 = 200 + 40 + 5 - 87 = - 80 - 7

245 = 200 + 40 + 5 - 87 = - 80 - 7 158 = 120 33 5

How to Build It

Number Sense Can’t Be Taught, It’s Caught

STRATEGIES Can’t Be Taught, They’re Caught

7

The emphasis is usually on PLACE

Emphasize VALUE

Stages of Interpretations of Numerals1.Whole Number

–The numerals represent a quantity in a symbolic representation 2.Positional Property

–The digit in the far right represents the ones place. The digit on the left is the tens place. The focus is on the position of the digit, not connecting it to the quantity.

3.Face Value –Knows that the digits can be named as ___ones or even ____ tens, but still is unable to connect the number represented by the 10’s digit is a multiple of 10.

4.Construction Zone – Knows the digit on the left represents sets of 10 objects and the digit on the right

represents the remaining single objects. 5.Understanding

–Students can partition the quantity into a tens part and a ones part. The quantity of objects corresponding to each digit can be determined even if the collection is partitioned into non-standard ways.

Ross, 1989

Place Value Chart

What does it mean to use a “base-10” number system?

Ten Thousands

Thousands Hundreds Tens Units Tenths Hundredths Thousandths Ten Thousandths

10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

100

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

101 100 10-1

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

102 101 100 10-1 10-2

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

103 102 101 100 10-1 10-2 10-3

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-4

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-41 1

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-410 1

1 1

1 10

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-4100 1

10 1

1 1

1 10

1 100

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-41000

1100 1

10 1

1 1

1 10

1 100

1 1000

Place Value Chart


Ten Thousands


10,000 1000 100 10 1 0.1 0.01 0.001 0.0001

104 103 102 101 100 10-1 10-2 10-3 10-410000

11000

1100 1

10 1

1 1

1 10

1 100

1 1000

1 10000

Place Value ChartTen

ThousandsThousands Hundreds Tens Units Tenths Hundredths Thousandths Ten

Thousandths

5



Thousandths

55 0



Thousandths

55 0

5 0 0



Thousandths

1 5 0 0

140 - 80

=14 tens = 8 tens

Ideas to Try

Bundling & UnBundling

7 Fosnot-Context for Learning

Let kids bundle & unbundle groups of 10, 100, 1000, etc.

7https://amzn.to/2ylVcMz

Bundling & UnBundling

https://amzn.to/2yfS04Y

https://amzn.to/2ylVcMz

https://amzn.to/2yfS04Y

5 ones 3 tens

Base Ten Riddles

7 Van de Walle, 2014

Early Elementary Examples •I have 2 tens and 13 ones. What am I? •I am 46. I have 3 tens, how many ones do I have? •What is 4 tens, 3 ones, and 2 hundreds?

Upper Elementary Examples •I have 30 tens, 5 hundreds, 9 ones, and 6 thousands. What am I?

•I have 39 ones, 5 hundreds, and 62 tens. How far from 3,000 am I?

• I am 11.05. I have 15 hundredths and 8 ones, how many tenths do I have?

Place ValueHow many tens are in 53? How many tens are in 243? How many tens are in 1,037?

1037.5 How much is the digit 3 worth? What place is the digit 1 in? How many tenths are in the number?

A candy factory had 48,638 candy bars to

put into boxes holding 100 candy

bars each. How many boxes will they need?

Candy Factory

7




STRATEGIES Can’t Be Taught, They’re Caught

Place ValueWITH

Incorporating Addition & Subtraction Strategies

Based On

CHRISTINA TONDEVOLD

incorporating addition & subtraction strategies based on ...€¦ · incorporating addition...

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