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QTEL UNIT OVERVIEW (Note: This QTEL unit is designed to accompany Seminar 8. It does not incorporate all instructional activities. It supplements the activities in Seminar 8).

Grade: 2

Content Area:

Mathematics

Unit: Seminar 8: Building the Relationship Between Addition and Multiplication

Unit Goals:

•SWABT to demonstrate the relationship between multiplication and addition.

•SWABT solve a multiplication word problem using a variety of strategies:

a. repeated addition*b. arrays (explicit instruction)c. pull down method d. distributive property (explicit instruction)

•number anchors (explicit instruction- into numbers they know= 2, 5, 10)

Example: Instead of 4 x 7, try 4 x 5 and 4 x 2e. commutative property

•SWBAT use their understanding of doubles (and doubles + 1) to determine whether a number up to 20 is even or odd (use calendar).

•SWBAT solve problems with multiples of 4 using doubles.

•SWBAT clearly explain their math reasoning using domain-specific vocabulary.

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STANDARDSMath Content Standards:

CCSS.Math.Content.2.0A.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

CCSS.Math.Content.2.0A.C.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.

Math Practice Standards

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. Look for and express regularity in repeated reasoning.

Listening/Speaking:

SL.2.1Participate in collaborative conversations with diverse partners about grade 2 topics and texts with peers and adults in small and larger groups. a. Follow agreed-upon rules for discussions (e.g.,gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). b. Build on others’ talk in conversations by linking their comments to the remarks of others. c. Ask for clarification and further explanation as needed about the topics and texts under discussion.

Writing:

W.2.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.

How will students demonstrate these standards? Math Story Problems Routines Participation in Aligned Activities Final Seminar Performance Task

Notes Vocabulary to Teach/Use

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•Start using “sum” and/or “product” instead of answer in some of your story problems.

•Get some more stickies. (Use Big Index Cards and Tape if no post its available).

•Label the corners of the classrooms.

•Create story problems with more than one step.

arraygroups of/sets ofbreak apart groupsPartial Product

odd/evencolumns/rows vertical/horizontalanchor or friendly numbersequals/same aspairs/doublesnumber sentencemultiplication

UNIT PLANNING: 3 MOMENT ARCHITECTUREGoals for Each MomentPREPARING THE LEARNER

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activate students’ prior, relevant knowledge establish an interest in and focus for the lesson focus their attention on the theme(s)/concepts to be explored introduce key ideas and language in context promote perspective and community building

INTERACTING WITH THE TEXTS/CONCEPTS text is deconstructed and students focus on understanding a key

section reconnect analyzed parts to the text as a whole, gaining deeper

understanding of the themes and concepts lead students one step closer to the attainment of lesson/unit goals

EXTENDING UNDERSTANDING apply newly gained knowledge to novel situation or to problem

solve. students use their understanding of the text(s) to create/re-

recreate a representation of important ideas connect new ideas to ideas gained through other lessons, content

areas, and life experiences, putting them all in perspective. write to represent new understandings or take a critical stance

Preparing Learner Tasks:x Preparing the Learners Task

Interacting with Task Extending Understanding Task

Name of Task Purpose of the Task4

Think-Pair-Share To get students to think about some of the important

concepts and use the vocabulary that they will encounter in this math seminar.

Task Description In partnerships, students reflect on the following prompts:

•When I hear the words “groups of” I think…

•When I see 4 x 6, I think…

*Higher Level Students During the “Pair” portion will say and write the answer to these prompts in their journals.

Possible Language Supports When I see ________, I think_________.

Interacting with the Text Task: Preparing the Learners Task

x Interacting with Task Extending Understanding Task

Name of Task 1 Purpose of the Task Students verbalize the reasoning for their thinking and

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Four Corners(5X during this seminar)

understanding.

Task DescriptionDisplay Four Corners problem on document camera.Give students 2 minutes to think about the problem independently. They can take their whiteboards with them to show their work.After 2 minutes, students are given the direction to explain their thinking.Teacher rotates through each group to support students.Whole group conversation/reflection.

(Be prepared to help structure the talk at each corner. Splitting groups? Who talks first?).

Four Corners 1If Marley found 4 boxes and there are 8 treats in each box, how many treats are there in all? (a and d are correct answers. Look for students who look confused and can’t decide where to go.) a. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 b. 4 + 8 c. 8 - 4 d. 4 x 8Go to the corner with the correct answer. Explain how you know.

LANGUAGE SUPPORT: In the story, I know that _______________.I know it is ____________ because _____________.I know it is not _____________ because _______________.

Four Corners 2(After you introduce “even” and “odd using the calendar)Which number sentence will have an “odd” sum? (a is the correct answer.) a. 11 + 12 b. 11 + 11 c. 56 + 56 d. 8 + 2Go to the corner with the correct answer. Explain how you know.

LANGUAGE SUPPORT: I know it is even/odd when ______________. I know it is even/odd because _______________.

Four Corners 3(After you teach the Distributive Property- “Break Apart Groups”…)How would you break apart 4 x 12 (a and c are correct answers. Look for students who look confused and can’t decide where to go.) a. 4 x 1 and 4 x 2 b. 4 x 10 and 4 x 2 c. 4 x 6 and 4 x 6 d. 4 x 12 and 4 x 12

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Go to the corner with the correct answer. Explain how you know.

LANGUAGE SUPPORT: I used friendly/anchor numbers to break apart ___(12)________. __(4 x 12)__ can be broken into _____________ and ______________.

Four Corners 4(After you teach arrays…) 5 x 3. How can you show this number sentence using an array? (Two right answers: b and c.) a. (insert array) 15 in a row b. (insert array) 5 x 3 c. (insert array) 3 x 5 d. (insert array) 2 rows x 5Go to the corner with the correct answer. Explain how you know.

LANGUAGE SUPPORT: The array that I picked shows ____________ rows and _________ columns.

Four Corners 5(After you have taught the strategies.)Solve 4 x 14. Which strategy worked best for you? (No right answer. Students are just verbalizing their thinking.) a. pull-down method b. array c. break apart groups (distributive property) d. Groups OfGo to the corner with the correct answer. Explain why this strategy worked for you.

LANGUAGE SUPPORT: I chose this strategy because…I agree with you because…So what you are saying is…(Invite a nonspeaker to participate… “_________, What do you think?”

Preparing the Learners Task


Name of Task 2

Academic Conversation(5X during this seminar- once each time a new target vocabulary is introduced)

Purpose of the Task Presenter- Shares problem-solving and uses target

vocabulary Listener- Listens attentively, tallies target vocabulary

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Task Description(REVIEW TALLY MARKS, PRIOR TO THIS ACTIVITY)

Students solve a story problem using a specific strategy independently.They work with a partner to engage in Academic Conversation.

Speaker •Share how you solved the problem with your partner. •Use the word _(strategy)_ in your explanation.

Listener •Listen carefully to your partner. •Ask your partner to clarify, when necessary. •Tally the number of times you heard your partner use _____________.

Possible Language SupportsIn the story problem, I know that…

The strategy I chose was ______________ . This worked because ________________. ORThe way I solved this problem was ___________________. This worked because _______________.

Our thinking was the same/different because __________________.



Name of Task 3

Picture This!

Purpose of the TaskInternalize the meaning of target vocabulary with the use of a visual representation (Picture Glossary).

Task DescriptionAs teacher introduces new vocabulary in the context of instruction,Students will create a visual representation for the target vocabulary.They will tab a page in their math journal that will serve as a picture glossary.

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REMINDERCreate a Target Vocabulary/ Strategy chart for Seminar 8

•array

•groups of

•break apart groups

•partial product

•repeated addition

Explain to a partner why you chose to represent the word with that picture.

Possible Routine: Guess someone’s picture- What vocabulary word is being represented? How do you know?

Possible Language Supports

This picture represents __________________. I think this because ________________.A(n) ______________ is/has __________________.I think this picture goes with this word because ________________.


x Interacting with Text Task

Extending Understanding Task

Name of Task 4

Collaborative Poster with Checklist and Round Robin

Purpose of the Task

Students represent graphically and symbolically the results of a story problem.

Task Description

Introduce Problem-Solving Checklist.Students will solve the story problem independently on a post-it. Assign A, B, C, D speakers to decide who goes first and in what order (Talk Structure).Speakers take turn sharing their solution to their problem. (The speaker has the floor. No interrupting)After everyone shares, they compare their solutions.The group combines parts of everyone’s ideas to build the most comprehensive solution.Each group member uses a different color marker and signs the poster.Each group presents.

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Possible Language SupportsWhen comparing solutionsOur thinking was the same/different because __________________.The strategy most of us used was _________________.I notice that ______________________.I had the same solution as _______________ because _____________.My solution was different than _______________’s because________________.

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Extending Understanding Task: Preparing the Learners Task

Interacting with Task x Extending Understanding Task

Name of Task

Gallery Walk with Checklist

Purpose of the Task

•Review the proficient expectations of the seminar. •Provide students the opportunity to reflect on these expectations. •Critically evaluate the work of their peers.

Task Description

Display one Collaborative Poster from each group.Review Problem-Solving Checklist.5 minutes to walk around and see all the posters.Assign each group a poster to evaluate. Give a few minutes so group members can complete their own individual evaluation (white paper).After a few minutes, the group works together to evaluate the poster. The group must reach a consensus/agreement on their evaluation (different color paper).Groups attach their evaluation to the poster.Groups go back to their original poster to review feedback. Whole group reflection.

Possible Language SupportsI notice that this group used _______________.

Examples of Multiple-Step Problems

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Problem-Solving Checklist:

Model/ pictureo Example:

Number sentenceo Example:

Strategyo Example:

Organized/circled answer/underline important parts

o Example: Using complete sentence

o Example:

There are 15 girls and 14 boys. They are going on a field trip. If 4 students fit in a car, how many cars do they need?

There are 6 juice boxes in a case. If we buy 4 cases, how many juice boxes will we have? If there are 32 students in a class, will there be enough for everyone?

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5 x 3How can you show this number sentence using an array?

A. B.

C. D.


“The array that I picked shows ____________ rows and _________ columns.”

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Four Corners 4

Solve 4 x 14. Which strategy worked best for you? A. pull-down methodB. arrayC. break apart groups D. groups of

Go to the corner with your answer. Explain why this strategy worked for you.

“I chose this strategy because _____________.”“I agree with you because _____________.”“So what you are saying is _______________.”(Invite a someone to participate). “_________, What do you think?”

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Four Corners 5

How would you break apart 4 x 12 ?

A. 4 x 1 and 4 x 2 B. 4 x 10 and 4 x 2 C. 4 x 6 and 4 x 6 D. 4 x 12 and 4 x 12


“I used friendly/anchor numbers to break apart ___________.”“__________ can be broken into _____________ and ______________.”

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Four Corners 3

Which number sentence will have an “odd” sum? A. 11 + 12 B. 11 + 11 C. 56 + 56 D. 8 + 2


“I know it is even/odd when ______________.” “I know it is even/odd because _______________.”

If Marley found 4 boxes and there are 8 treats in each box,

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Four Corners 2

Four Corners 1

how many treats are there in all?

A. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 B. 4 + 8 C. 8 - 4 D. 4 x 8


“In the story, I know that _______________.”“I know it is ____________ because _____________.”“I know it is not _____________ because _______________.”

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Problem-Solving ChecklistModel/ Picture

o Example:

Problem-Solving ChecklistModel/ Picture

o Example:

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