SECOND GRADESession 3

Vacaville USD

March 26, 2015

AGENDA• Problem Solving• Subtraction Facts and Computation

– Word Problems– Number Line– Multiple Representation– Multi-Digit

• Money• Arrays and Repeated Addition

Norms• We are each responsible for our own

learning and for the learning of the group.• We respect each others learning styles

and work together to make this time successful for everyone.

• We value the opinions and knowledge of all participants.

Problem Solving

Kentucky Department of Education• Mathematics Formative Assessment Lessons

– Concept-Focused Formative Assessment Lessons

– Problem Solving Formative Assessment Lessons• Designed and revised by Kentucky DOE

Mathematics Specialists – Field- ‐tested by Kentucky Mathematics

Leadership Network Teachers

http://teresaemmert.weebly.com/elementary-formative-assessment-lessons.html

A Snail in the WellPrimary/Intermediate Grades

• Problem Solving Formative Assessment Lesson

• Lesson Format–Pre-Lesson (about 15 minutes)

Analyze Student Work

Suggestions for feedback• Common issues• Suggested questions and prompts

A Snail in the WellPrimary/Intermediate Grades

• Problem Solving Formative Assessment Lesson

• Lesson Format–Pre-Lesson (about 15 minutes)–Lesson (about 1 hour)–Follow-Up (about 10 minutes)

A Snail in the Well

Snail in a Well – Second Grade

• A snail is at the bottom of a well that is 10 feet deep.– What’s a snail?– What is a well?– What is 10 feet?

Snail in a Well – First Grade

• What’s a well?

Snail in a Well

• A snail is at the bottom of a well that is 10 feet deep.

• Each day he crawls up 2 feet.• How many days will it take him to get to

the top of the well?

Snail in a Well

• A snail is at the bottom of a well that is 10 feet deep.

• Each day he crawls up 3 feet BUT each night he slides back 1 foot.

• How many days will it take him to get to the top of the well?

Estimation and Number Sense

Developing Number Sense

Estimate• How many goldfish are in my “pond”?

46

Developing Number Sense

Estimate• How many Easter eggs will it take to fill the

small vase?

53

Estimation

• How many cheeseballs are in the vase?

183

Estimation

• How many peanut m&m’s are in the vase?

• Are there more m&m’s than cheeseballs or less?–How do you know?

463

How many green marshmallows will fit on the skewer?

How many green marshmallows will fit on the skewer?

How many green mallows are needed to complete the 4-leaf clover?

How many green mallows are needed to complete the 4-leaf clover?

How many green marshmallows are inside the glass?

Solving Subtraction Problems

Using a Number Line

• Find 43 on the number line.–What “tens numbers” is it between?–How is it from 40? How do you know?–How far is it from 50? How do you know?

Using a Number Line

• Find 68 on the number line.–What “tens numbers” is it between?–How is it from 60? How do you know?–How far is it from 70? How do you know?

Subtracting on a Number Line

7 – 3 =• Walking on a number line• Moving on a number line• Drawing on a number line

What’s My Number Sentence

• I started at 4 and walked until I got to 7. How far did I walk?– What the answer?– How did you solve the problem?– What number sentence could I use to solve

the problem?

What’s My Number Sentence

• I have 8 cookies. I gave 2 of them to my brother. How many cookies do I have now?– What the answer?– How did you solve the problem?– What number sentence could I use to solve

the problem?

Solving Problems UsingMultiple Representations

Multiple Representations

• Build/Act It Out (Concrete)• Draw (Representational)• Ten Frame (Concrete or Representational)• Number Bond (Abstract/Symbolic)• Number Line (Concrete/Representational)

Building and Practicing Facts

• Shauna has 12 Easter Eggs to decorate. She gives some to her little sister and then decorates the rest. If she decorates 8 eggs, how many eggs did she give to her sister?

• Taken From/Change Unknown

• Maria and Jorge are decorating Easter Eggs. Maria has decorated 14 eggs and Jorge has decorated 8 eggs. How many more eggs has Maria decorated?

• Compare/Difference Unknown

• Max has decorated 12 Easter Eggs. This is 3 more than his cousin decorated in the same amount of time. How many eggs did his cousin decorate?

• Compare/Smaller Unknown

• Matt has 5 of the Reptarland toys from Burger King. He wants to collect 2 complete sets for him and his brother. If he needs 8 toys to complete each set, how many more toys does he need to get?

• Multi-Step• Add To/Change Unknown

Practicing Facts

13 – 8 =

Practicing Facts

Practicing Facts

Practicing Facts

716

Practicing Facts

Multi-Digit Subtraction

Examining the Standards• Which standards require students to be

“fluent”?• Which standards expect students to be

moving towards fluency but not totally proficient?

• Which standards expect students to understand the concept?

• HOW DO YOU KNOW?

Tools

• Ten Frames• Base 10 blocks• Number Line• Base 10 Shorthand• Decomposing and Composing Numbers

Developing Subtraction

• Concrete– Base 10 Blocks

• Representational– Base 10 Shorthand– Number Line

Developing Subtraction

• Abstract– Recording process from concrete or abstract

stages– Number Bonds– Alternative Algorithms– Variations on the Traditional Algorithm

(1) 74 – 48

• Build 74 using base 10 blocks• Trade 1 ten for 10 ones• Remove 4 tens and 8 ones

How could we record this?• Representation• Abstract / Symbols

(2) 74 – 48

• Build 74 using base 10 blocks• Take 1 of the tens, move it to the ones,

and cover up 8– How many ones are left?

• Remove 4 tens

How could we record this?• Representation• Abstract / Symbols

(3) 74 – 48

• Locate 74 on the number line• Move to 70. • How many spaces did you move?• How many more do you need to move?• Move a distance of 40?

– How can you quickly move 40?– Where do you land?

(3) 74 – 48

• How many more do you need to move?• Now, where do you land?

How could we record this?• Representation• Abstract / Symbols

(4) 74 – 48

• Locate 74 on the number line• Move a distance of 40?

– How can you quickly move 40?– Where do you land?

• Move a distance of 8?– How can you quickly move 8?– Where do you land?

• Recording?

(5) 74 – 48

• What are some other strategies that students might use?

Exploring Strategies

• Do each problem at least 3 different ways– How do you record?

• 68 – 35• 81 – 29• 463 – 247• 624 – 296

Money

Money

MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Coins

• Jordan found five coins at the bottom of his bookbag. Three are dimes and two are nickels. How much money did Jordan find?

Coins

• Jordan found five coins at the bottom of his bookbag. He told his friend that he found 50¢. What coins did Jordan find?

Money

• What skills do students need to have to count coins?– How can you practice these skills before

students begin to learn money?– How can you continue to develop these skills?

Coins

Joel went to the store and bought three items. He bought a pencil for a dime, an eraser for 38¢, and a pencil sharpener for a quarter. • How much money did Joel spend at the

store?• How did he make the 38¢, assuming he

used the least amount of coins possible?

• Groups of 3– Buyer 1– Buyer 2– Seller

49¢

Buyer 1: Count out exactly 49¢.Buyer 2: Hand the Seller a $1 billSeller: Give Buyer 2 change for $1.

Check

32¢

Buyer 1: Count out the exact price.Buyer 2: Hand the Seller a $1 billSeller: Give Buyer 2 change for $1.

Check

$3.78

Buyer 1: Count out the exact price.Buyer 2: Hand the Seller a $5 billSeller: Give Buyer 2 change for $5.

Check

Money

The First Grade classes raised $56 during

the school fund raiser. The Second Grade

classes raised $84 during the school fund

raiser. How much more money did the

Second Grade classes raise than the First

Grade Classes?

Money

The Second Grade classes raised $84

during the school fund raiser. This was $28

more than the Third Grade classes raised.

How much did the Third Grade classes

raise?

Arrays

Arrays

OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Materials Needed: Tiles• Count out 12 tiles.• Use those 12 tiles to make an array. • Describe the array.

– Prompts if needed: How many rows are there? How many columns are there?

• Draw a picture of your array. • Write an equation that represents your

array.

After students has finished the first array.• Count out another 12 tiles.• Use those 12 tiles to make a different

array. • Describe the array.

– Prompt if needed: How many rows are there? How many columns are there?

• Draw a picture of your array. • Write an equation that represents your

array.

Materials: Tiles.• Make an array that has 4 rows with 5 tiles

in each row.• Draw a picture of your array.• How many tiles did you use?• Write an equation that represents your

array.

Once students have finished the original array.• Can you make another array that uses all

20 of the tiles?• Describe your array.• Draw a picture of your array.• Write an equation that represents your

array.

How Many Stars?

Write an equation.Can you write another equation?