**Let's Go on a Treasure Hunt**

Focus Standard Clusters

These groups of standards correspond to some of the most important topics and skills for students to master in each grade or course. Focus clusters in grades 3-8 from 2012-13 remain, and additional clusters have been added to those grade levels. All other grade levels or courses have four new focus clusters.

Make and Take Tools

Magnetic Boards

Tens Frames

Number Lines

Hundred Chart

Graph paper

Any other requests?

Model Drawing - this afternoon

Strategies for Modifying Tasks to Increase the Cognitive Demand

Ask students to create real-world stories for “number only” problems.

Include a prompt that asks students to represent the information another way (with a picture, in a table, a graph, an equation, with a context).

Include a prompt that requires students to make a generalization.

Use a task “out of sequence” before students have memorized a rule or have practiced a procedure that can be routinely applied.

**Treasures**

What treasures did you find today?

What treasures are you most excited to share with your class?

Math Practices

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. (www.corestandards.org)

Kindergarten Focus Clusters

Know number names and the count sequence.

Count to tell the number of objects.

Understand addition as putting together and adding to and understand subtraction as taking apart and taking from.

Work with numbers 11-19 to gain foundations for place value.

Fluency K.OA.A.5: Add/Subtract within 5

1st Grade Focus Clusters

Represent and solve problems involving addition and subtraction.

Understand and apply properties of operations and the relationship between addition and subtraction.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Fluency 1.OA.C.6: Add/Subtract within 10.

2nd Grade Focus Clusters

Represent and solve problems

involving addition and subtraction.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Relate addition and subtraction to length.

Fluency 2.OA.B.2: Add/Subtract within 20 (Know single digit sums from memory).

Fluency 2.NBT.B.5: Add/Subtract within 100.

3rd Grade Focus Clusters

Represent and solve problems involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Develop understanding of fractions as numbers.

Geometric measurement: understand concepts of area and relate area to multiplication and addition.

Fluency 3.OA.C.7: Multiply/Divide within 100 (Know single digit products from memory)

3.NBT.A.2: Add/Subtract within 1000

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4th Grade Focus Clusters

Extend understanding of fractions equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Use the four operations with whole numbers to solve problems.

Generalize place value understanding for multi-digit whole numbers.

Fluency 4.NBT.B.4: Add/Subtract within 1,000,000

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5th Grade Focus Clusters

Use equivalent fractions as a strategy to add and subtract fraction.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Understand the place value system.

Perform operations with multi-digit whole numbers and decimals to hundredths.

Fluency 5.NBT.B.5: Multi-digit multiplication

Accountable Talk Features & Indicators

Accountability to the Learning Community,

Math Practice #?

Active participation in classroom talk.

Listen attentively.

Elaborate and build on each others’ ideas.

Work to clarify or expand a proposition.

Accountability to Knowledge,

Math Practice #?

Specific and accurate knowledge.

Appropriate evidence for claims and arguments.

Commitment to getting it right.

Accountability to Rigorous Thinking,

Math Practice #?

Synthesize several sources of information.

Construct explanations and test understanding of concepts.

Make & Take: Talk Starters Ring

1. Independently, write at least 5 talk starters for the Math Practices and Accountable Talk Features & Indicators (try to address as many as you can)

2. Work with a partner/small group to write at least one talk starter for each Math Practice and Accountable Talk Indicator.

3. We will work together to create a group list.

As making your rings, think and discuss, "How will I implement/address Math Practices & Accountable Talk in my classroom?"

Math Practice Cubes

Create your own math practice cube to use with your class.

Strategies Continued

Eliminate components of the task that provide too much scaffolding

Adapt a task so as to provide more opportunities for students to think and reason – let students figure things out for themselves.

Create a prompt that asks students to write about the meaning of the mathematics concept.

Add a prompt that asks students to make note of a pattern or to make a mathematical conjecture and to test their conjecture.

Strategies Continued

Include a prompt that requires students to compare solution paths or mathematical relationships and write about the relationship between strategies or concepts.

Select numbers carefully so students are more inclined to note relationships between quantities (e.g., two tables can be used to think about the solutions to the four, six, or eight tables).

Rationale

Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask. (NCTM, 1991) Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge. (NCTM, 2000) Questions are one of the only tools teachers have for finding out what students are thinking. (Michaels, 2005)

3rd Grade Repeated Addition as Multiplication EnVision Practice

Cindy wants to plant 12 flowers in her garden. She wants her flowers to be in rows with the same number of flowers in each row. How many ways could she do this? Use models to represent your answer. Write an equation to go with each model.

Changed to a High Level Task

Now it is your turn!

Using the EnVision practice problem for your grade level, create a higher level task to use in your classroom.

Rationale

All tasks are not created equal−different tasks require different levels and kinds of student thinking.

Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Olivier, & Human, 1997

Rationale

If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 1996