Standards Academy

Grades 3 & 4 Day 4

Welcome BackReflection on yesterday:

• 4 Point Evaluation

• Parking Lot

Objectives• Understand a variety of types and purposes of

assessment.• Create formative assessments.• Understand the fluency requirements of 3rd and 4th

grade.• Understand effective strategies for building

fluency.

Assessment Affinity Map1. On sticky notes, write about a type of assessment you give,

include a brief description. Use a new note for each type of assessment.

2. Silently put all of your notes on the group’s chart paper.3. Still silently: As a group organize your stickys into natural

categories. As long as you do not talk, feel free to move any post-it note to any place. Move yours, and those of others, and feel free to do this. Do not be offended if someone moves one of your sticky notes.

4. Organize the categories into nice columns, as a group converse about the columns and come up with a name for each one.

Assessment Vocabulary SortYour team is now going to sort various assessments. Each assessment has three cards associated with it.

For example let’s look at multiple choice

Multiple-Choice An assessment question that requires the

student to choose the correct answer from a limited number of possibilities, usually four

or five.

This assessment is easy to score and lends itself to easier data organization and

analysis. Teachers may identify common misconceptions by incorrect answer

choices chosen by students.

Assessment Affinity Map1. Return to your group’s chart paper and discuss what you

learned from the sorting activity.2. Make any changes your team would like.3. Identify one or two spokespeople to present your poster to

the whole group. Try to speak to the following points.a) Describe the categories and assessments.b) What were some difficulties your team had?c) What impact did the sorting activity have on your poster?

Think about a time in your life when you were evaluated or assessed on a task or assignment and felt like you did NOT receive useful or accurate information back relating to your

mastery of the project or skill. Create a T-Chart list all the characteristics of that

ineffective assessment down one side of the chart.In contrast, think about a time in your life when you were

evaluated or assessed on a task or assignment and felt like you DID receive useful or accurate information back relating

to your mastery of the project or skill. Complete the opposite column. So what’s the

difference?

Effective Assessment T-Chart

Why Assess?Consider what you discovered through your

own experiences in assessment when addressing the following questions with a

partner:1. What is the definition of assessment?2. What do we assess in mathematics?3. What are the purposes of assessment?4. How is assessment useful for teachers?5. How is assessment useful for students?6. What methods are used for assessment?7. When do we assess?

Discuss:  What do you notice about frequency and types

of assessment? How do you use each of these types of

assessment in your classroom, school, district? What are the benefits and challenges of

assessing in a variety of ways?

Assessment

Formative Assessmenthttps://www.teachingchannel.org/videos/teacher-assessment-strategy

https://www.teachingchannel.org/videos/class-warm-up-routine

Think-Pair-Share• What do these videos have in common?• Are there pieces that you could use in your

practice

Formative Self Assessment

Formative Self Assessment

Formative Assessment

Name:MondayShow the repeated addition for 5 x 4. 1 2 3

Name:TuesdayUse grouping to show 4 x 3. 1 2 3

Name:WednesdayDraw an array to show 2 x 5 = 10. 1 2 3

Name:ThursdayChange the multiplication equation into a division sentence.

5 x 3 = 15 1 2 3

• Index Cards• Sticky Notes• Smart Response Clickers• Journal Reflections• What have you used in your classrooms?

Discussion: What information could you gain about your students’ understanding by having them complete exit tickets or quick formative assessments during or after lessons?

Other Ideas for QUICKFormative Assessment

Consider resources you already have…..

Math Expressions 4th Grade

Go Math 3rd Grade

Infographic Gallery StrollThere are 4 posters posted around the room.

1. Find one poster and form a group.2. Take a few minutes to review the infographic3. As a group write 4 meaty questions pertaining to the

infographic, and post the questions near the sign.4. When signaled move to the next poster.5. As a group discuss the questions posted by the previous

group.6. Repeat rotations until you return to your original poster.7. Whole group share out.

It’s your turn to put it all together.

In partners or triads you are going to write some examples of formative assessments.

• Identify a standard and skill to assess.• Consider any prerequisite and corequisite skills.• Consider DOK and include varied levels of rigor.• Consider appropriate models and vocabulary.• Use any and all the resources you have gathered this

week.

Computational Fluency

On a piece of paper write your own definition of math fluency.

Turn to a partner and share what you have in common what is

different?

The word fluent is used in the standards to mean fast and

accurate. Fluency involves a mixture of just knowing some

answers, knowing some answers from patterns, and knowing

some answers from the use of strategies.”

“Procedural Fluency refers to knowledge of procedures,

knowledge of when and how to use them appropriately and

skill in performing them flexibly, accurately and

efficiently.”

Drill is extremely limited in terms of developing fluency. Building meaning

through mental strategies, practice with using efficient mental strategies and making connections between various

derived fact strategies has consistently shown to increase fluency. More

importantly, students using derived fact strategies are able to transfer and retain

their knowledge long-term more effectively than students using

memorization and drill.

(Baroody, 1985; Brownell, 1935; Dawson & Ruddell, 1955; Fuson, 1992; Henry & Brown, 2008); Thornton, 1978)

How does this change your definition of fluency?

What do you agree with?What do you want to argue?What do you want to incorporate into your practice?

A Case for Derived Facts and Strategies

Relying on memorization alone students would have to memorize

100 different facts! x 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Using the commutative property alone will leave 55 facts to memorize!

 x 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Using anchor facts alone student will still need to memorize 36 facts!

 x 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Using derived facts alone student will still need to memorize 39 facts!

(Double Double & 5 Plus One More)x  1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

When flexibly combining multiple strategies there are very few if any facts to

memorize!x  1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

3 3 6 9 12 15 18 21 24 27 30

4 4 8 12 16 20 24 28 32 36 40

5 5 10 15 20 25 30 35 40 45 50

6 6 12 18 24 30 36 42 48 54 60

7 7 14 21 28 35 42 49 56 63 70

8 8 16 24 32 40 48 56 64 72 80

9 9 18 27 36 45 54 63 72 81 90

10 10 20 30 40 50 60 70 80 90 100

Double and Double again 4 x 6 = (2x6) + (2x6) = 12 + 12 = 24Try 4 x 9

Half then double

6 x 8 = (3x8) + (3x8) = 24 + 24 = 48Try: 6 x 6

Double and one more set

3 x 7 = (2x7) + 7 = 14 + 7 = 21Try: 3 x 9

Distributive Property 7 x 6 = (5x6) + (2x6) = 30 + 12 = 42Try: 8 x 8

On your grid paper, draw a few 7 x 12 arrays.

Think of some easy, related facts that would helpyou solve 7 x 12 if you didn’t know the answer.42

Use your grid paper arrays to draw what thesefacts strategies would look like if you ‘sliced’ or‘split’ or ‘added to’ your arrays.

1. Identify a group time keeper and scribe.2. Read the text silently.3. While reading highlight:

a. A significant sentenceb. A significant phrasec. A significant word

Text Rendering Protocol

1. In the first round each person in the group shares their important sentence. The scribe writes each down.

2. In the second round each person shares their important phrase. The scribe writes each down.

3. In the third round each person shares their important word. The scribe writes each down

4. The group then takes a minute to review the notes the scribe has taken and discuss what they heard and what it says about the document.

5. The group debriefs on “How does this article align with what we have learned this week?”

Wrap Up & ReflectWrite on the following reflection prompts:• This week something that shifted in my

thinking regarding math instruction is…

• These are things I want to try or ways I want to improve my practice…