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In this presentation we will learn addition and subtraction

1.

2.
Problem Solving

3.
Challenges students face when

solving applications in mathematics

Brainstorm 5 or more major

challenges students face when solving

rigorous problems in mathematics.

You will share with your shoulder

partner when think time is up and I

say go.

Think Time begins now…

solving applications in mathematics

Brainstorm 5 or more major

challenges students face when solving

rigorous problems in mathematics.

You will share with your shoulder

partner when think time is up and I

say go.

Think Time begins now…

4.
What are the characteristics of

good problem solvers?

Write down as many

characteristics that you can think

of.

You have 2 minutes

good problem solvers?

Write down as many

characteristics that you can think

of.

You have 2 minutes

5.
An Effective Problem Solver

Reads the problem carefully

Defines the type of answer that is required

Identifies important information and words

Accesses background knowledge regarding a similar

situation

Eliminates extraneous information

Uses a graphic organizer

Sets up the problem correctly

Uses mental math and estimation

Checks the answer for reasonableness

Make mental pictures (Visualize)

Reads the problem carefully

Defines the type of answer that is required

Identifies important information and words

Accesses background knowledge regarding a similar

situation

Eliminates extraneous information

Uses a graphic organizer

Sets up the problem correctly

Uses mental math and estimation

Checks the answer for reasonableness

Make mental pictures (Visualize)

6.
UNDERSTAND PLAN

SOLVE CHECK

SOLVE CHECK

7.

8.

9.
In grades K-5, the TEKS outline seven process

standards, which “describe ways in which students are

expected to engage in the content.”

The process standards were intentionally listed at the

beginning of the knowledge and skills for each

grade level to emphasize the integrated importance of

the process standards.

These process standards represent the thinking,

habits, and processes through which a student

engages with mathematics to

acquire and demonstrate mathematical thinking.

9

standards, which “describe ways in which students are

expected to engage in the content.”

The process standards were intentionally listed at the

beginning of the knowledge and skills for each

grade level to emphasize the integrated importance of

the process standards.

These process standards represent the thinking,

habits, and processes through which a student

engages with mathematics to

acquire and demonstrate mathematical thinking.

9

10.
NEW process standards

Problem-Solving Model

Current TEKS Revised TEKS (2012)

Understanding the Problem Analyzing given information

Making a plan Formulating a plan or strategy

Carrying out the plan Determining a solution

Evaluating the solution for Justifying the solution

reasonableness Evaluating the problem-solving

process and the

reasonableness of the solution

Problem-Solving Model

Current TEKS Revised TEKS (2012)

Understanding the Problem Analyzing given information

Making a plan Formulating a plan or strategy

Carrying out the plan Determining a solution

Evaluating the solution for Justifying the solution

reasonableness Evaluating the problem-solving

process and the

reasonableness of the solution

11.
Problem Solving…Revised TEKS

Solve problems with guidance that K.1B/1.1B/2.1B

incorporate the process of Use a problem‐solving model

understanding the problem,

that incorporates analyzing

making a plan, carrying out the

given information,

plan, and evaluating the solution

of reasonableness formulating a plan or

strategy, determining a

solution, justifying the

K.13C/1.11C/2.12C solution, and evaluating

Select or develop and use an the problem‐solving process

appropriate problem‐solving plan

and the reasonableness of

or strategy including drawing a

picture, looking for a pattern,

the solution

systematic guessing and checking,

or acting it out in order to solve a

Solve problems with guidance that K.1B/1.1B/2.1B

incorporate the process of Use a problem‐solving model

understanding the problem,

that incorporates analyzing

making a plan, carrying out the

given information,

plan, and evaluating the solution

of reasonableness formulating a plan or

strategy, determining a

solution, justifying the

K.13C/1.11C/2.12C solution, and evaluating

Select or develop and use an the problem‐solving process

appropriate problem‐solving plan

and the reasonableness of

or strategy including drawing a

picture, looking for a pattern,

the solution

systematic guessing and checking,

or acting it out in order to solve a

12.
Today’s TEKS Focus

Kindergarten First Grade Second Grade

Modeling Addition and Modeling Addition and Use Equations to Represent

Subtraction Subtraction Problems

K.3 (A) The student is 1.3 (B) use objects and 2.4 (C) solve one-step and multi-

expected to: pictorial models to solve step word problems involving

model the action of joining to word problems involving addition and subtraction within

represent addition and the joining, separating, and 1,000 using a variety of strategies

action of separating to comparing sets within 20 based on place value, including

represent subtraction. and unknowns as any one of

the terms in the problem algorithms.

such as 2 + 4 = [ ]; 3 + [ ] =

7; and 5 = [ ] - 3

Use story mats and Use organizers to bridge Use story mats, UPSC model,

manipulatives to develop the development of and manipulatives to use

joining and separating up addition and subtraction to equations.

to 20 objects. the abstract of writing

number sentences.

Kindergarten First Grade Second Grade

Modeling Addition and Modeling Addition and Use Equations to Represent

Subtraction Subtraction Problems

K.3 (A) The student is 1.3 (B) use objects and 2.4 (C) solve one-step and multi-

expected to: pictorial models to solve step word problems involving

model the action of joining to word problems involving addition and subtraction within

represent addition and the joining, separating, and 1,000 using a variety of strategies

action of separating to comparing sets within 20 based on place value, including

represent subtraction. and unknowns as any one of

the terms in the problem algorithms.

such as 2 + 4 = [ ]; 3 + [ ] =

7; and 5 = [ ] - 3

Use story mats and Use organizers to bridge Use story mats, UPSC model,

manipulatives to develop the development of and manipulatives to use

joining and separating up addition and subtraction to equations.

to 20 objects. the abstract of writing

number sentences.

13.

14.
5 E Model Addition & Subtraction (Kindergarten)

Engage Use questions eliciting prior knowledge about experiences

going to zoos and being in plays.

Read the story.

Explore & Reread the story with students acting it out physically and

Explain with manipulatives of a zoo mat and animal cards pointing

out separating, joining, and relating to the size of the group

(linking cubes are also available).

Elaborate 1 Students will use animal cards or linking cubes.

Elaborate 2 Students will again experience joining and separating of sets

with a beach mat and sea shells.

Evaluate Students choose beach mat or zoo mat and are given 3

scenarios to solve with manipulatives; students will create a

scenario.

Engage Use questions eliciting prior knowledge about experiences

going to zoos and being in plays.

Read the story.

Explore & Reread the story with students acting it out physically and

Explain with manipulatives of a zoo mat and animal cards pointing

out separating, joining, and relating to the size of the group

(linking cubes are also available).

Elaborate 1 Students will use animal cards or linking cubes.

Elaborate 2 Students will again experience joining and separating of sets

with a beach mat and sea shells.

Evaluate Students choose beach mat or zoo mat and are given 3

scenarios to solve with manipulatives; students will create a

scenario.

15.
5 E Model Addition & Subtraction (Grade 1)

Engage Use questions eliciting prior knowledge about experiences with

zoos and being in plays. Read the story while students physically

act it out with manipulatives.

Explore 1 Addition will be modeled with the visual of the part/part whole

mat and zoo mat with the poem.

Explain 1 Read the story and experience using the part/part whole mat

with the addition portion of the story.

Explore 2 Subtraction will be modeled with the visual of the part/part whole

mat and zoo mat with the poem.

Explain 2 Finish the story and experience using the part/part whole mat

with the subtraction portion of the story.

Elaborate Students will embellish the zoo story by drawing the new story

and writing the matching number sentence.

Evaluate The students will create and write a new scenario, then give the

story to a partner and let the partner write the number sentence.

Engage Use questions eliciting prior knowledge about experiences with

zoos and being in plays. Read the story while students physically

act it out with manipulatives.

Explore 1 Addition will be modeled with the visual of the part/part whole

mat and zoo mat with the poem.

Explain 1 Read the story and experience using the part/part whole mat

with the addition portion of the story.

Explore 2 Subtraction will be modeled with the visual of the part/part whole

mat and zoo mat with the poem.

Explain 2 Finish the story and experience using the part/part whole mat

with the subtraction portion of the story.

Elaborate Students will embellish the zoo story by drawing the new story

and writing the matching number sentence.

Evaluate The students will create and write a new scenario, then give the

story to a partner and let the partner write the number sentence.

16.

17.
Linking Cubes or Cards to Represent

1 gorilla – 1 blue cube

2 elephants – 2 white cubes

3 tigers – 3 orange cubes

4 parrots – 4 red cubes

5 monkeys – 5 brown cubes

1 gorilla – 1 blue cube

2 elephants – 2 white cubes

3 tigers – 3 orange cubes

4 parrots – 4 red cubes

5 monkeys – 5 brown cubes

18.

19.
One gorilla is out of his cage,

Oh my, what a rage!

Oh my, what a rage!

20.

21.
Two elephants followed in line,

Parading, strutting, looking fine!

Parading, strutting, looking fine!

22.

23.
Three tigers let out a roar,

As they join the fun galore.

As they join the fun galore.

24.

25.
Four parrots flew the coop,

What a crazy looking group.

What a crazy looking group.

26.

27.
There are 10 animals out of their cages. If the 5 monkeys

join them how many animals will be out of their cage?

UNDERSTAND PLAN

I need to find… Use my cubes or

cards to join the

How many animals monkeys with the

are out of their cage other animals and

in all count them.

SOLVE CHECK

Students use mats to

solve. 15 IIII IIII

IIII IIII

join them how many animals will be out of their cage?

UNDERSTAND PLAN

I need to find… Use my cubes or

cards to join the

How many animals monkeys with the

are out of their cage other animals and

in all count them.

SOLVE CHECK

Students use mats to

solve. 15 IIII IIII

IIII IIII

28.
Which manipulative

is easier to use and

to understand the

concepts for this

is easier to use and

to understand the

concepts for this

29.

30.

31.
Part-Part-Whole Mat

32.
Five monkeys

scream and shout.

It doesn’t take long for them to

get out!

scream and shout.

It doesn’t take long for them to

get out!

33.

34.
Five monkeys scream and shout.

It doesn’t take long for them to get out!

10 5

+ =

15

It doesn’t take long for them to get out!

10 5

+ =

15

35.
Cling! Clang! It’s dinner time!

Five monkeys swing home in

rhyme.

Five monkeys swing home in

rhyme.

36.

37.
- = 10

5

5

38.
Four parrots hungry for seed

Quickly fly back to feed.

Quickly fly back to feed.

39.

40.
Three tigers smell red meat,

As they swiftly spring to their feet.

As they swiftly spring to their feet.

41.

42.
Two elephants run for food.

They must eat not to be rude!

They must eat not to be rude!

43.

44.
One gorilla, sad and blue,

What do you think he should do?

What do you think he should do?

45.
How did we use

visuals to move the

students from the

concrete to the

abstract level of

visuals to move the

students from the

concrete to the

abstract level of

46.
Abstract/

Activity Concrete Pictorial

Generalization

Zoo story – Acting •Kids are experiencing Act It Out Animal • Students begin to

it out as in a play a tactile and kinesthetic Card Placards generalize that joining

activity. • Students model the means that the group

poem wearing is getting larger.

•Kids see a physical pictures of animals

representation and around their neck. • Students begin to

interaction with the generalize that

story. separates means the

group is getting

•The purpose of acting smaller.

it out is to allow all

students to create a • Students can also

common experience on generalize that if no

which they can draw. animals join, then the

group stays the same.

•Acting it out provides

students an opportunity • Students begin to

to connect language generalize what

with action. happens to the group

size and the

reasonableness to

their answers.

Activity Concrete Pictorial

Generalization

Zoo story – Acting •Kids are experiencing Act It Out Animal • Students begin to

it out as in a play a tactile and kinesthetic Card Placards generalize that joining

activity. • Students model the means that the group

poem wearing is getting larger.

•Kids see a physical pictures of animals

representation and around their neck. • Students begin to

interaction with the generalize that

story. separates means the

group is getting

•The purpose of acting smaller.

it out is to allow all

students to create a • Students can also

common experience on generalize that if no

which they can draw. animals join, then the

group stays the same.

•Acting it out provides

students an opportunity • Students begin to

to connect language generalize what

with action. happens to the group

size and the

reasonableness to

their answers.

47.
Time for a brain break…

47

47

48.
Second Grade Lesson

49.
Use Equations to Represent Problems (Grade 2)

Engage Use questions eliciting prior knowledge about

addition and subtraction. Show video to

excite students.

Explore Have the students choral read the problem

given in the video. Students will use a story

mat, manipulatives and the UPSC model.

Explain Addition and subtraction will be modeled with

the visual of the part/part whole mat and

story mat with the poem.

Elaborate Students will use their UPSC model to work through

the problem and write corresponding equations.

Evaluate Students can create their own story problem

and ask a partner to create the equation.

Engage Use questions eliciting prior knowledge about

addition and subtraction. Show video to

excite students.

Explore Have the students choral read the problem

given in the video. Students will use a story

mat, manipulatives and the UPSC model.

Explain Addition and subtraction will be modeled with

the visual of the part/part whole mat and

story mat with the poem.

Elaborate Students will use their UPSC model to work through

the problem and write corresponding equations.

Evaluate Students can create their own story problem

and ask a partner to create the equation.

50.
Use equations to represent problems.

http://www-k6.thinkcentral.com/content/hsp/math/texas_math_2015/tx/gr2/vid

eo_based_projects_se_9780544103672_/mediaPlayerWindow.html?url=http:

//link.brightcove.com/services/player/bcpid1861182355001?bckey=AQ~~,AA

AA2fV0xfE~,Tmydk9UFFWVJKhSHBEdCMdi5yCXNIT1G&bctid=ref:En_317

50

http://www-k6.thinkcentral.com/content/hsp/math/texas_math_2015/tx/gr2/vid

eo_based_projects_se_9780544103672_/mediaPlayerWindow.html?url=http:

//link.brightcove.com/services/player/bcpid1861182355001?bckey=AQ~~,AA

AA2fV0xfE~,Tmydk9UFFWVJKhSHBEdCMdi5yCXNIT1G&bctid=ref:En_317

50

51.
There were some ducks in a pond. Four more

ducks joined them. Then there were 13 ducks in

the pond. How many ducks were in the pond at

first?

UNDERSTAND PLAN

I need to find…

How many ducks were in Use my part-part-whole

the pond before 4 more mat and cubes because I

came. have the whole and I am

? + 4 = 13 missing a part.

I am missing a part.

SOLVE CHECK 9 + 4 = 13

Students use mats to solve. 13 - 4 = 9

Students can draw a picture. There were 9 ducks in the

pond at first.

Students can also draw a picture

here.

ducks joined them. Then there were 13 ducks in

the pond. How many ducks were in the pond at

first?

UNDERSTAND PLAN

I need to find…

How many ducks were in Use my part-part-whole

the pond before 4 more mat and cubes because I

came. have the whole and I am

? + 4 = 13 missing a part.

I am missing a part.

SOLVE CHECK 9 + 4 = 13

Students use mats to solve. 13 - 4 = 9

Students can draw a picture. There were 9 ducks in the

pond at first.

Students can also draw a picture

here.

52.
Emphasis on Questioning

Plan questions while preparing

lessons

Increase wait time

Ask for paraphrases

Record your lessons to monitor

levels of questioning

Plan questions while preparing

lessons

Increase wait time

Ask for paraphrases

Record your lessons to monitor

levels of questioning

53.

54.

55.
Focal Areas

55

55

56.
We need your input.

Professional Learning Surveys:

We have created some surveys so that we can elicit

feedback from all of the participants about the

trainings they attend. Visit the website below and

complete the appropriate survey(s).

The surveys will be open until April 18 and

reminders will go out through Mark Thomas next

week, but we would like for you to complete your

survey today if possible.

Professional Learning Surveys:

We have created some surveys so that we can elicit

feedback from all of the participants about the

trainings they attend. Visit the website below and

complete the appropriate survey(s).

The surveys will be open until April 18 and

reminders will go out through Mark Thomas next

week, but we would like for you to complete your

survey today if possible.