GRADE 3 MATH: COOKIE DOUGH

UNIT OVERVIEW

This packet contains a curriculum-embedded CCLS aligned task and instructional supports. The task is embedded in a 4-5 week unit on interpreting and linking representations, modeling situations, solving non-routine problems and justifying arguments of multiplication and division.

TASK DETAILS

Task Name: Cookie Dough

Grade: 3

Subject: Mathematics

Task Description: The tasks in the unit access the full range of Depth of Knowledge, including Recalling and Recognizing, Using Procedures, Explaining, Concluding and Making Connections, Extensions and Justifying.

Standards: 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects

each. 3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in eachshare when 56 objects and partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays,and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.3.OA.5 Apply properties or operations as strategies to multiply and divide.3.OA.6 Understand division as an unknown-factor problem.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication anddivision (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letterstanding for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain themusing properties of operations.

Standards for Mathematical Practice: MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model using mathematics.

1

Engage: 3rd Grade Sample Task

Cookie&Dough&

&Clear&Creek&School&is&fundraising.&&&

They&are&selling&Cookie&Dough&in&tubs.&

&

&

&

&

&&

Chocolate&Chip&Cookie&Dough&&

$5&a&tub&

Peanut&Butter&Cookie&Dough&

$4&a&tub&

Oatmeal&Cookie&Dough&$3&a&tub&

&

&

1. Jill&sold&2&tubs&of&Oatmeal&Cookie&Dough.&&&

How&much&did&she&raise?&&&& & & $&____________________________&

&

&

&

2. Joe&sold&4&tubs&of&Peanut&Butter&Cookie&Dough&and&4&tubs&of&Chocolate&Chip&Cookie&Dough.&&&

How&much&money&did&he&raise&in&all?&$&_________________________________&

&

Show&how&you&figured&it&out.&& & & & & & & & & & &

&

&

&

&

&

&

&

&

&

&

&

4

&

3. Jade&sold&only&Peanut&Butter&Cookie&Dough.&&She&raised&$32.&&&&

How&many&tubs&did&she&sell?&__________________&tubs&

&

Show&how&you&figured&it&out.&

& & & & & & & & & & & & &

&

&

&

&

&

&

&

&

4. Jermaine’s&mother&loves&oatmeal&cookies.&&She&has&$20.&to&spend.&&&&

What&is&the&greatest&number&of&tubs&of&Oatmeal&Cookie&Dough&she&can&

buy?&

__________________________&tubs&

&

Explain&how&you&figured&it&out.&

&

______________________________________________________________________________________&

______________________________________________________________________________________&

______________________________________________________________________________________&

______________________________________________________________________________________

&

5

GRADE 3 MATH: COOKIE DOUGH

RUBRIC The rubric section contains a scoring guide and performance level descriptions for the Cookie Dough task. Scoring Guide: The scoring guide is designed specifically to each small performance task. The points highlight each specific piece of student thinking and explanation required of the task and help teachers see common misconceptions (which errors or incorrect explanations) keep happening across several papers. The scoring guide can then be used to refer back to the performance level descriptions. Performance Level Descriptions: Performance level descriptions help teachers think about the overall qualities of work for each task by providing information about the expected level of performance for students. Performance level descriptions provide score ranges for each level, which are assessed using the scoring guide.

6

COMMON CORE CURRICULUM EMBEDDED TASK

Grade 3 Math: Cookie Dough

Cookie Dough Scoring Guide

Cookie Dough Rubric The core elements of performance required by this task are: • work with multiplication and division in a real context Based on these, credit for specific aspects of performance should be assigned as follows:

points

section points

1. Gives correct answer: $6.00 and shows some correct work such as: 3 + 3 = 6

1 1

2. Gives correct answer: $36.00

Shows work such as: 4 x 4 and 4 x 5

1

1

2

3. Gives correct answer: 8

Shows work such as: 32 ÷ 4

1

1

2

4. Gives correct answer: 6

Gives a correct explanation such as: The most her mother can buy is 6 tubs because I counted by 3s and she can buy 6 but doesn’t have enough for 7 or, I counted 3, 6, 9, 12, 15, 18, 21. She doesn’t have 21.

1

1

2

Total Points 7

7

Task Analysis Tool Understanding Language Initiative, Stanford University

Name of Task: Cookie Dough Task Grade Level: Third Subject: Math

Task Analysis

Step Guiding Questions and Resources

Analysis

Ste

p 1

: E

xam

ine

an

d

Ide

nti

fy A

pp

rop

ria

te

Inst

ruct

ion

al T

ask

Guiding Questions: Is/does this task: Clear in its expectations? Grade-level appropriate? Aligned to the standards? Require students to use language and

analytical skills to demonstrate their content knowledge?

Is this an appropriate task for analysis? Why?

Ste

p 2

: Id

en

tify

Ta

sk D

em

an

ds

Guiding Questions: • Write down everything that students

need to demonstrate, know, or do in order to successfully complete this task.

• To do this, read (or watch) the task instructions.

Resources: • For Content Knowledge: Common

Core State Standards, Next Generation Science Standards, or other relevant standards (e.g., district, state, etc.)

• For Analytical Skills: Depth of Knowledge (DOK) Levels

• For Language: Language Functions and Forms PDF

What do students need to do and know in terms of…?

Content Knowledge Analytical Skills Language

Ste

p 3

: Id

en

tify

Dis

cip

lin

ary

Pra

ctic

e(s)

Guiding Question: What disciplinary practice(s) are most relevant to this task? Resources: Core Disciplinary Practices PDF Interactive Correspondence between

Practices, Tasks, and Functions PDF

What are the relevant disciplinary practices for this task: Math Practice 1-Make sense of problems and solve them Math Practice 2-Reason abstractly and quantitatively (More quantitatively) (Figure out the problem with only the oatmeal dough cost) Math Practice 3- Construct Viable arguments and critique the reasoning of others (just the first part of this practice…the answer is their argument and the explanation is the support.) Math Practice 4-Model with mathematics (analytical-decide which quantities are relevant & analyze relationships among quantities) Math Practice 6-Attend to precision (Make claims that apply to a precise set of situations) ELA Practice 6- Use English structures to communicate context specific messages (written explanation of how the student found the answer,) and infer meaning of crucial academic and discipline-specific vocabulary from context (i.e. greatest.)

Ste

p 4

: Id

en

tify

EL

P S

tan

dar

d(s

)

Guiding Questions: What English Language Proficiency Standards are reflected in this task? Which of these ELP standards do you feel comfortable measuring or intend to assess? Resources: • The ELP Standards • Alternative Organization of

Standards • The K-12 Practices Matrix

What are the relevant ELP standards for this task? Please include your reasoning behind selecting these standards.

ELP Standard Your Reasoning ELP 1 * Construct meaning for a grade-appropriate math

problem (some teachers felt it would be appropriate to assess this standard, others felt it would too hard to tease out if it was constructing meaning or not knowing which math operation to use.)

ELP 3 * Write about grade-appropriate complex informational texts

ELP 4 Construct a written claim (answer) and support it with evidence (written explanation)

ELP 7 Adapt language choices to purpose (math writing) ELP 8 * Determine the meaning of words and oral phrases in

texts ELP 9 * Create clear and coherent grade-appropriate text

(recounting a sequence of events with transitional words) First, I did…then I …

* Standards teachers felt one could measure adequately in this task

Third Grade: Cookie Dough Student Work

Third Grade: Cookie Dough Student Work

Understanding Language/SCALE, Stanford University

Using ELP Standards Level Descriptors (PLDs) to Interpret Student Work

Understanding Language/SCALE, Stanford University

October 2016

Task: Cookie Dough - Math Grade Level: 3-5

Step 1 Examine the Identified ELP Standard(s) and Corresponding Level Descriptors

Consulting ELP Standards and Level Descriptors

Examine the identified ELP Standard(s) and corresponding level descriptors for the task

If there are many applicable standards, choose one or two that relate to your students’ areas of growth.

Notes: Sample 1

Previous teacher panel selected ELP Standards 1,3, 8, and 9 for this task.

Natalie – Standards 1 and 8 are implied. But 3 seems to be most appropriate to assess.

Brenda – Standard 1 – construct meaning is implied. But 3 seems to be the best match to assess the task.

Jobi – 3 is best match for work sample.

After looking at student work more closely, teachers switch to Standard 9 for assessment purposes.

Sample 2:

Shaeley – because less text, makes you wonder the level of proficiency of student and whether they are understanding the prompt. Explanation is sparse.

Natalie - Because of sparseness – hard to tell thought process of student.

Brenda – student seems to have misunderstood the question.

Jobi - How do you tell whether it’s a language or content issue?

Shaeley – can see that the student knows basic math, but didn’t understand what the question was asking.

Have to tease out whether it’s mathematical or whether it’s language.

Teachers agree that ELP Standard 1 is the best to assess.

Step 2 Interpret Student Work Using the Standards Level Descriptors

Understanding Language/SCALE, Stanford University

Using ELP Standards Level Descriptors as rubrics to interpret student work

Do the same standards apply when you examine your students’ output?

What level(s) most accurately describe your students’ work?

Remember that the interpretation only tells you the level of this specific piece of student work; your students’ levels might shift based on different tasks or learning objectives.

Identify patterns (similarities or differences) in your students’ work if you are interpreting multiple pieces.

Notes: Sample 1:

Brenda – In standard 3, the focus is on informational texts, and she wonders if explaining fits in there.

Shaeley – descriptors of PLD for Standard 3 aren’t very descriptive.

Natalie – Wonders if task lends itself to 2 because explaining is in that standard.

Jobi – Looking at Standard 8 and 9 and wondering if this might be more about form than function.

Teachers look at student work again and decided that Standard 9 would be better assessed.

Shaeley – recounting sequence and using linking words are informative for this work sample. Leans toward level 3 because of common linking words.

Brenda surprised not to see “and” or other simple linking words. When seems to be the only linking word to link two events.

Natalie – Places student at beginning of level 3.

All teachers agree on beginning level 3. Sample 2:

Natalie- Student was able to pull out a key word, so she thinks level 1.

Brenda – Student was able to understand “explain how you…” that some explanation or process was being asked for because of the word “because”. Maybe they understand the main topic or message which would put them at level 2.

Natalie – and the answer makes sense with what the question asks. It’s not a way off number given the problem.

Jobi – are they emerging or evolving set?

Shaeley- lean toward level 2 because she doesn’t see key details in student work.

Brenda – wonders if student understands the task and fell down at some point in content.

Teachers decide on level 2.

Step 3 Identify strategies to support student needs Identifying instructional supports to improve student learning

Use the identified level (and perhaps the next level) to provide student with formative feedback.

Use the identified patterns in student work to plan for instructional adjustments.

Consult relevant state/district resources for suggested strategies.

Notes:

Understanding Language/SCALE, Stanford University

Sample 1:

Stronger and Clearer Together – having opportunity to explain to peers and pick up language from peers.

Reviewing sequence words

Anchor charts

Sentence/discourse frames using sequence words Sample 2:

Three reads strategy to get them to slow down and read multiple times to get more meaning out of question.

Engage: Using Formative Assessment and ELP Standards to Guide Instruction Cookie Dough Lesson Plan

Grade: 3 Subject: Math Objective: Students will be able to speak and write about how they solved a math word problem. Related ELP/CCSS Standards: • 3.OA.3 Use multiplication and division within 100 to solve word problems in situations

involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

• 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

• Math Practice 1-Make sense of problems and solve them • Math Practice 2-Reason abstractly and quantitatively • Math Practice 3- Construct Viable arguments and critique the reasoning of others • Math Practice 4 – Model using mathematics • ELP 2-3.1 An ELL can construct meaning from oral presentations and literary and

informational text through grade appropriate listening, reading, and viewing. • ELP2-3.3 An ELL can speak and write about grade-appropriate complex literary and

informational texts and topics Text: Cookie Dough task math word problems Materials: Cookie Dough worksheet, chart paper, markers, and handout Focus: Three reads strategy Introduction We have been working on math problems related to selling cookie dough and practicing addition and multiplication. In our last class, you worked on a few questions on a worksheet. I noticed that you were able to show how you figured it out, and today, we are going to focus on explaining how you figured it out. Let’s start with #4. Teach/Model We are going to start by reading the question three times (Show chart paper with steps). Each time I will ask you to answer a specific question. (Read #4 aloud). With your elbow partner, discuss “what is this situation about?” (Ask for a few volunteers and chart the answers on paper - debrief)

Now look up here at #4 and let’s read it again as a class (Read). Many math stories(?) have information about quantities (numbers) and the units that are being counted. Talk to your partners again about “what are the quantities in this situation and how are they related?” (Ask for a few volunteers and chart the answers on paper - debrief) We’re going to read the question again, this time, I would like you to think about all the possible questions we could ask of this situation. Could I have _______ read the question for the class? Talk to your partners about “what are all the mathematical questions we could ask in this situation?” (Ask for a few volunteers and chart the answers on paper - debrief) Now take a few minutes to complete the question if you did not get to finish last time and make any changes to your explanation. Share your answer with your partner. Student Practice Now, you are going to practice showing and explaining how you figured out the answer with a different problem: Taylor sold only Chocolate Chip Cookie Dough. He raised $40. How many tubs did he

sell? Show and explain how you figured it out. Take turns reading with your partner and don’t forget to paused after each read to take some notes on your handout!

Student Handout Chocolate Chip Cookie Dough $5 a tub

Peanut Butter Cookie Dough $4 a tub

Oatmeal Cookie Dough $3 a tub

Taylor sold only Chocolate Chip Cookie Dough. He raised $40. How many tubs did he sell? Show and explain how you figured it out. Read 1: What is the situation about?

Read 2: What are the quantities in this situation?

Read 3: What are questions we could ask?

Answer: _________ tubs Show how you figured it out. Explain how you figured it out. ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________