Contributed by:
In this presentation we will learn addition and subtraction
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…
4.
What are the characteristics of
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)
6.
UNDERSTAND PLAN
SOLVE CHECK
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
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
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
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.
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.
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.
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
19.
One gorilla is out of his cage,
Oh my, what a rage!
21.
Two elephants followed in line,
Parading, strutting, looking fine!
23.
Three tigers let out a roar,
As they join the fun galore.
25.
Four parrots flew the coop,
What a crazy looking group.
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
28.
Which manipulative
is easier to use and
to understand the
concepts for this
32.
Five monkeys
scream and shout.
It doesn’t take long for them to
get out!
34.
Five monkeys scream and shout.
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.
38.
Four parrots hungry for seed
Quickly fly back to feed.
40.
Three tigers smell red meat,
As they swiftly spring to their feet.
42.
Two elephants run for food.
They must eat not to be rude!
44.
One gorilla, sad and blue,
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
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.
47.
Time for a brain break…
47
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.
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
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.
52.
Emphasis on Questioning
Plan questions while preparing
lessons
Increase wait time
Ask for paraphrases
Record your lessons to monitor
levels of questioning
56.
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