INTERMEDIATE MATHResources and Building Content
Knowledge
Education Transformation Office
Common Board Configuration (CBC)
Exit Slip:
•Revisit Essential Question
AGENDA:
I Do:•Review focus group materials
We Do:•Teach One/Learn One Activity •Math Content Training
They Do:•Map out how you’re going to teach the beginning of the year concepts.You Do:•Processing Time: Answer the essential question•Homework Instruction
Vocabulary: Pacing guide, Skills Sheets, Journal Entries , Scope and Sequence, Rubric, Essential Labs, NGSSS, Item Specs
ESSENTIAL QUESTION: How can exploring the math content and resources help me to be an effective teacher?
Objective: Today we will explore the math content and review resources to help implement best practices to teach the content effectively.
BENCHMARK: Math Resources and Content.
BELL RINGER:
DATE: August , 2013
Introductions: 3 – 2 - 1 Activity
3-2-1
Set 3 Goals for this school year
Write 2 actions that will assist you in
meeting your goals
Write 1 challenge that may
Encounter
ESSENTIAL QUESTION:
How can exploring the math content and resources help me to be an effective teacher?
What’s New and Continuing with ETO Elementary Math?
2013-2014 School Year
Full implementation of Common Core in the GO Math series.
Reflex math- Computer program for fluency
New Teacher Lead Center (TLC) packets Newly created bellringers by benchmark
infusing basic skills for practice New Think Central dash boards iReady
What’s NEW???
GO MATH 3rd Grade “Old vs. New”
GO MATH / ThinkCentral.com
Go Math textbooks are all correlated to Common Core.
Schools will receive updated Common Core Teacher’s Editions
You will continue to have access to the “Old GO MATH” with the NGSSS through thinkcentral.com
GO MATH Technology Correlations
Math Focus Group Created Materials
Pacing Guide Revisions Skills Sheets Independent Centers Binder Journal Entries Success Academy Lessons
Pacing Guide Revisions New Common Core Pacing Guides NGSSS Blended Curriculum New NBC Learn Video Links Lesson Combination Suggestions
Skills Sheets-Teacher Edition
Skills Sheets-Student Friendly
Independent Centers Binder
TEACH ONE, LEARN ONE
TEACH ONE, LEARN ONE
Use your popsicle stick to determine which group you are in.
Everyone will all be in groups of three. Every 3 minute segment, one person will be the
teacher, another person will be the student, and one could be the observer.› The teacher will teach the student a lesson on any
preferred subject. › The student will take notes. › The observer will watch the behaviors.
After three minutes you will switch roles. Continue to rotate until you have been all three roles.
Instructions of Collaborative Strategy
TEACH ONE, LEARN ONE What to do?
Wait until you’re told to begin. Once you get a signal to begin, you will write a response to a question for two minutes non-stop onto a sheet of paper.
TEACH ONE, LEARN ONE
What is Teaching?(Two Minutes)
TEACH ONE, LEARN ONE
What is Learning?(Two Minutes)
TEACH ONE, LEARN ONE
Now, discuss your answers with a shoulder partner.
You can revisit your two answers. Has your answer changed from the two question? If so, take two minutes to reflect and change your
answer.
DIGGING DEEPER INTO THE MATH
CONTENT 3rd Grade
TOPIC IAddition and Subtraction within 1,000
DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade
TOPIC I
Addition and Subtraction within 1,000
New Edition Common Core TextbookMACC.3.NBT.1.1, MACC.3.NBT.1.2, MACC.3.OA.4.8, Infusing the NGSSS MA.3.A.6.1 and MA.3.A.4.1
• Numbers1. Place Value2. Read3. Write4. Compare5. Order6. Inequalities symbols (<, >,
=, =)7. Real-World contexts
• Operations1. Addition2. Subtraction
• Estimation Strategies1. Rounding 2. Compatible Numbers3. Reasonableness4. Grouping 5. Decimals (context of money
that estimate to whole dollar
• Problem Solving (Rountine and Non-Routine)
1. Real-World content 2. Methods to determine
solutions1. Tables2. Charts3. Lists4. Searching for Patterns
3. Explain the method used to solve a problem
TOPIC I ESSENTIAL CONTENT INCLUDES:
Item Specs
Algebra –
Number, Operations, & Statistics
ITEM SPECS for MA.3.A.4.1
• Students may extend numeric or graphic patterns beyond the next step, or find one or more missing elements in a numeric or graphic pattern.
• Students will identify the rule for a pattern or the relationship between numbers.
BENCHMARK CLARIFICATIONWhat must students be able to do?
MA.3.A.4.1
CONTENT LIMITSMA.3.A.4.1
• Items may use numeric patterns, graphic
patterns, function tables, or graphs. (bar graphs, picture graphs, or line plots only)
• Numeric patterns should be shown with 3 or more elements.
• Graphic patterns should be shown with 3 or more examples of the patterns repeated.
• Students should not be asked to extend the patterns more than 3 steps beyond what is given or to provide more than 3 missing elements.
What does it look like?MA.3.A.4.1
What does it look like?MA.3.A.4.1
LLook for a pattern or rule:
Rule: Multiply by 5
X 5 =
X 5 =
X 5 =
X 5 =
45
What are good strategies? MA.3.A.4.1
Read each problem carefully and know what’s being asked.
Students need to find a rule for the pattern.
Use the number pairs. Apply the pattern or rule to each relationship and think of an operation that will help find the missing number.
Students need to practice showing their work to avoid simple mistakes.
Activities… MA.3.A.4.1Chairs Around a Table:
Students will:
• Identify and extend a linear pattern involving the number of chairs that can be placed around a series of square tables.
• Describe linear patterns using words or symbols.
Materials: • Pattern Blocks (squares and triangles).
Using a context of chairs around square tables, students will be exposed to different linear patterns in this lesson. The patterns may vary slightly from situation to situation, where the students are allowed to determine a solution in multiple ways, in the end leading to an intuitive understanding of perimeter.
At Pal-a-Table, a new restaurant in town, there are 24 square tables. One chair is placed on each side of a table. How many customers can be seated at this restaurant? Show an arrangement of one table with four chairs. Draw a demonstration on the white board or tech board. Or use pattern blocks or other transparent manipulatives on the overhead projector.
Activities MA.3.A.4.1 cont…
Sample of 1 table with 4 chairs arrangement
When all students understand how chairs are placed, ask, "If there were 24 tables in a room, how many chairs would be needed?"
Have students make a table showing the pattern and finding the rule. Depending on students’ understanding of multiplication, they may immediately realize that the answer is 24 × 4 = 96.
Ask students to create a number sentence that will help solve for the missing number.
Activities MA.3.A.4.1 cont…
Activities MA.3.A.4.1 cont…
From the table, students should realize that the number of chairs is equal to four times the number of tables. Alternatively, they might recognize that each time a table is added, four chairs are added. This is a good opportunity to reinforce the connection between multiplication and repeated addition.
Teachers should ask students to explain their observations. "What is the pattern? How can you find the number of chairs for any number of tables?" [Multiply the number of tables by 4. If there are 24 tables, for instance, the number of chairs is 96. If there are n tables, the number of chairs is 4n.]
Item Specs
Algebra –
Number, Operations, & Statistics
ITEM SPECS for MA.3.A.6.1
BENCHMARK CLARIFICATIONWhat must students be able to do?
MA.3.A.6.1
• Students can use the
following estimation strategies when representing, comparing, and computing numbers through the hundred thousand:
› Clustering› Reasonableness› Chunking› Using a reference› Unitizing› Benchmarks› Compatible
numbers› Grouping› Rounding
What Are The Content Limits?MA.3.A.6.1
Numbers may be represented flexibly; for example 947 can be thought of as 9 hundreds, 4 tens, and 7 ones; 94 tens and 7 ones; or 8 hundreds 14 tens and 7 ones
Items may include the inequality symbols( >, <, =, =)
Items will not require the estimation strategy to be named
Front-end estimation will not be an acceptable estimation strategy
Decimals may be used in the context of money that estimate to a whole dollar
What does it look like?MA.3.A.6.1
What does it look like?MA.3.A.6.1
2,000
1,000
2,000
2,000+
7,000
Round to the nearest hundreds place value.
What Are Good Strategies?MA.3.A.6.1
Always have students draw the place value chart
When writing in expanded form, add the zeros after the place value
Use the “Dip” chant Use the rounding wrap (for example: 4
or less, let it rest. 5 or more raise the score)
In order for students to be successful with addition and subtraction, they need a firm comprehension of place value. In this lesson, students extend their understanding of place value to numbers through hundred thousands.
Activities… MA.3.A.6.1
Have the students pair up in twos. They can rotate and make their own Egyptians numbers and guess the value.
Activities MA.3.A.6.1 cont…
Let’s take a look at Lesson 1.4
Mental Math Strategies for Addition
TOPIC IINumbers through 100, 000
DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade
TOPIC II
Numbers through 100,000Old Edition Next Generation Sunshine State Standards Textbook (ONLY)MACC.3.NBT.1.1, MACC.3.NBT.1.2, MACC.3.NBT.1.3, MACC.OA.4.8Infusing the NGSSS MA.3.A.6.1 and MA.3.A.6.2
• Numbers1. Place Value2. Read3. Write4. Compare5. Order6. Inequality symbols (<, >, =,
=)7. Real-World contexts
• Operations1. Addition2. Subtraction
• Estimation Strategies1. Rounding 2. Compatible Numbers3. Reasonableness4. Grouping 5. Decimals (context of money
that estimate to whole dollar
• Problem Solving (Rountine and Non-Routine)
1. Real-World content 2. Methods to determine
solutions1. Tables2. Charts3. Lists4. Searching for Patterns
3. Explain the method used to solve a problem
TOPIC II Essential Content Includes:
Item Specs
Algebra –
Numbers through 100,000
ITEM SPECS for MA.3.A.6.2
BENCHMARK CLARIFICATIONWhat must students be able to do?
MA.3.A.6.2
• Students will solve non-routine problems in situations where tables, charts, lists, and patterns could be used to find the solutions.
CONTENT LIMITSMA.3.A.6.2
• Items should require students to solve non-
routine problems and not align with the clarifications of MA.3.A.4.1 (extending a graphic pattern or identifying a simple relationship [rule] for a pattern).
What does it look like?MA.3.A.6.2
What does it look like?in red
Charles
Erin
Gayle
Paco
Erin
Erin
Erin
Gayle
Gayle
Gayle
Paco
Paco
Paco
Charles
Charles
Charles
3 (students
circled)
2 (students circled)
1(students circled)
+ 0 (students
circled)
6 different pairs of two students can be made
What are good strategies?MA.3.A.6.2
Always have students draw a chart or make an organized list
Make sure students are using a strategy that they understand and can demonstrate and verbalize on their conclusion.
Students need to check if answer make sense.
ACTIVITIES… MA.3.A.6.2 Students may work in small groups
Example: A frog in a pit tries to go out. He jumps 3 steps up and then slides 1 step down. If the height of the pit is 21 steps, how many jumps does the frog need to make?
Example: Show 5 different combinations of US coins that total 53¢.
Example: The 24 chairs in the classroom are arranged in rows with the same number of chairs in each row. List all of the possible ways the chairs can be arranged.
revise
Mathematical Practices
“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.”
~ Bill McCallum
Standards for Mathematical Practices
Mathematical Practices
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Topic I and IIMathematical Practices
MP 6: Attend to precision
Mathematically proficient students can…
use clear definitions and mathematical vocabulary to communicate their own reasoning
careful about specifying units of measure and labels to clarify the correspondence with quantities in a problem
Topic I and IIMathematical Practices
MP 7: Look for and make use of structure
Mathematically proficient students can…
look closely to determine possible patterns and structure (properties) within a problem
analyze patterns and apply them in appropriate mathematical context
Professional Development PodcastMP 6 and 7
Let’s Watch one together!
How did you see the practice being implemented?
TOPIC IICollect and Analyze Data
DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade
TOPIC III
Collect and Analyze Data
New Edition Common Core TextbookMACC.3.MD.2.3, MACC.3.MD.2.4Infusing the NGSSS MA.3.S.7.1
• Picture Graph (Pictographs)1. Sample size (No more than 200)
2. Parts of a graph3. Keys (Scale of 1, 2, 5, 10)4. Interpreting and comparing
information5. Generating Questions6. Colleting responses7. Displaying data (interpret, create,
and explain) 8. Real-World / mathematical contexts
• Bar Graphs1. Sample size (No more than 1,000)2. Parts of a graph 3. Scale (units of 1, 2, 5, 10, 50, or
100)4. Interpreting, create, and
comparing information5. Generating questions6. Collecting responses 7. Display data (interpret, create, and
explain) 8. Real-World / mathematical contexts
• Frequency Tables – Sample size (no more than 200)
• Line Plots – Sample size (no more than 200)
• Problem Solving (Routine and Non-Routine)
1. Real-World content 2. Methods to determine
solutions1. Tables2. Charts3. Lists4. Searching for Patterns
3. Explain the method used to solve a problem
TOPIC III Essential Content Includes:
Item Specs
Sample question
Data Analysis-
ITEM SPECS for MA.3.S.7.1
BENCHMARK CLARIFICATIONWhat must students be able to do?
MA.3.S.7.1
• Students will construct, analyze, and draw conclusions from frequency tables, bar graphs, picture graphs, and line plots.
• Students will analyze data to supply missing data in frequency tables, bar graphs, picture graphs, and line plots.
Students may be required to choose the most appropriate data from observations, surveys, and/or experiments
Items may assess identifying parts of a correct graph and recognizing the appropriate scale
The increments on the scale are limited to units of 1, 2, 5, 10, 20, 25, 50, or 100
CONTENT LIMITSMA.3.S.7.1
Pictographs can use keys containing a scale of 1, 2, 5 , 10
The data presented in graphs should represent no more than five categories
The total sample size for bar graphs should be no more than 1, 000
The total sample size should be no more than 200 for frequency tables, pictographs, and line plots.
Addition, subtraction, or multiplication of whole numbers may be used within the item.
CONTENT LIMITS cont…MA.3.S.7.1
What does it look like?
Frequency Table
Bar Graph
Show students how to use process of elimination. Since there were 4 scones sold, then we could eliminate A and D.
And there are 8 brownies sold. Answer choice B shows that.
Then we verify if Muffin showed 2 sold and Cookies shows 10 sold.
8
4
4
108
6
10
8
What are some good strategies to consider:
Extracting data from a Bar Graph:
• Read the title first and then the scale to know what and how much the increments are.
• Write the corresponding value next to or on top of each bar.
• Pay attention to what is being asked to answer.
Frequency Table
Pictograph
What does it look like?
Extracting data from a pictograph:
It is very IMPORTANT that students read the title first and then the key so they know what and how many the symbols represent.
Make a routine for students to write the corresponding number next to each activity. Have them write the total.
In this case, students will use a frequency table to match up the correct pictograph.
EXAMPLE:
104
10
102
5
104
10
58
*
Pay attention to the half symbols.
What are some good strategies to consider:
Extracting data from a Pictograph:
• It is very IMPORTANT that students read the title first and then the key so they know what and how much the symbols represent.
• Write the value next to each symbol and then find the total for each row of symbols.
• Pay attention to what is being asked to answer.
What does it look like?
Line plots may be confusing to some students. It is easy to mix up the numbers below the number line and the X’s above it.
Students need to remember that the numbers below the number line are like the categories in a pictograph or a bar graph. In a line plot, these categories are numerical. The number of X’s above each number on the number line tells how many times this number or category occurs.
Answer: C
The most X’s
What are some good strategies to consider:Extracting data from a Line Plot:• Remember that the numbers
below the number line are like the categories in a pictograph or a bar graph. In a line plot, these categories are numerical.
• The number of X’s tells how many times the number or category occurs.
• Pay attention to what is being asked to answer.
Topic III Mathematical Practices
MP 1: Make sense of problems and persevere in solving them.
Mathematically proficient students can…
explain the meaning of the problem
monitor and evaluate their progress “Does this make sense?”
use a variety of strategies to solve problems
Topic III Mathematical Practices
MP 4: Model with mathematics.
Mathematically proficient students can…
apply mathematics to solve problems that arise in everyday life
reflect on their attempt to solve problems and make revisions to improve their model as necessary
Professional Development PodcastMP 1 and 4
Let’s Watch one together!
How did you see the practice being implemented?
Activities for Data Analysis You could have the kids survey others in the class for selected
questions - do you have pets, favorite food, type of ice cream etc. From the info collected, create a bar graph. You could give the kids suggested topics but let them pick their own questions.
You can also have them build individual graphs by rolling dice. Make dice that fit with your theme. Give each student a blank graph and let them label the columns (or you can do this part). I use this at a center and the kids roll a die and record the roll on the graph. This week we are studying jobs that people do. I have a graph with pictures of a doctor, police officer, firefighter, teacher, and a postal worker. The die is labeled with these pictures also. The students take turns rolling the die until everyone has rolled and recorded 10 times on their own graph. They should all different.
TOPIC IIIMultiplication
What must students be able to do?
Model multiplication, including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement and partitioning.
What are the benchmark clarifications?
What does it look like?
What does it look like?
3 groups of 2
+ +
2 + + 2 2
What are good strategies?
Combinations-Make a tree diagram to show every combination
Use the finger multiplication trick for 9s and 6s-10s
Circle key words to help indicate the operation used.
Essential Question:
How can exploring the math and science content and resources help me to be an effective teacher?
Left Side of Interactive
Student Notebook (ISN)
ETO Elementary Collaboration Website
Build, Sustain, Accelerate
You can find this presentation in addition to all curricular resources on our very
own ETO Collaboration WebsitePlease visit us at:
http://www.etomiami.com/
QUESTIONS/CONCERNS