Common Core MathDavid LaiChristine Cho

Objectives Investigate Mathematical Practices Investigate Domains and Cluster

Standards for Number and Operations Base Ten.

Understand Grade Level Progression

CCSS Math Paradigm Shift Equip students with expertise that will

help them succeed in doing and using mathematics not only across K-12 mathematics curriculum but also in their college and career work.

College instructors rate the Mathematical Practices as being of higher value for students to master in order to succeed in their courses than any of the content standards themselves.

CCSS Math Paradigm Shift Develop deep understanding in

mathematics using: Conceptual Understanding Procedural Fluency

Deliberate attention and implementation on the CCSS Mathematical Practices.

CCSS Math Paradigm Shift How should students engage with

mathematics tasks and interact with their fellow students?

How well do we engage to develop students’ engagement in mathematics reflecting the CCSS mathematical Practices?

Standards for mathematical practices are not a checklist of teachers to dos, but rather they are processes and proficiencies for students to experience and demonstrate as they master the content standards

Organization of Mathematical Practices Overarching Habits of Mind Reasoning and Explaining Modeling and Using Tools Seeing Structure and Generalizing

Organization of Mathematical Practices

Overarching Habits of Mind

1.Make sense of problems and persevere in solving them.

6. Attend to precision

Reasoning and Explaining

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

Modeling and Using Tools

4. Model with mathematics.

5. Use appropriate tools strategically.

Seeing Structure and Generalizing

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Overarching Habits of Mind Use problem solving tasks and activities

to challenge students to persevere. Design lessons where students will need

to struggle to find the answers. We want students to overcome

challenges on their own rather than giving them the answers.

Overarching Habits of MindMP 1: Make sense of problems and persevere in solving them. Students make conjectures about the

meaning of a solution and plan a solution pathway.

Students try special cases or simpler forms to gain insight. (They hypothesize and test conjectures.)

Students monitor and evaluate their progress and discuss with others.

Students understand multiple approaches and ask the questionm “Does this solution make sense?”

Team Planning Questions That Promote CCSS Mathematical Practice 1 As we develop common tasks and problems to be

used during the unit, we should consider: 1. Is the problem interesting to students?

Does the problem involve meaningful mathematics?

Does the problem provide an opportunity for students to apply and extend mathematics?

Is the problem challenging for students? Does the problem support the use of multiple

strategies or solution pathways? Will students’ interactions with the problem and

peers reveal information about their mathematics understanding?

Overarching Habits of MindMP 6: Attend to Precision Students communicate precisely to others. Students use clear definitions of terms in

discussing their reasoning. Students express numerical answers with a

degree of precision appropriate for the problem context.

Students calculate accurately and efficiently. Students are careful about specifying units of

measure and using proper labels.

Team Planning Questions That Promote CCSS Mathematical Practice 6 What is the essential student vocabulary for this

unit, and how will our team assess it? What are the expectations for precision in

student solution pathways, explanations, and labels during this unit?

How will students be expected to accurately describe the procedures they use to solve tasks and problems in class?

Will student work as it relates to in- and out-of-class problems and tasks require students to perform calculations carefully and appropriately?

Will students’ team and whole-class discussions reveal an accurate use of mathematics?

Math Progression K-5Number and Operations in Base Ten

Kindergarten – Number and Operations in Base Ten In Kindergarten, teachers help children lay

the foundation for understanding: Base-ten system by drawing special

attention to 10. Children learn to view the whole numbers 11

through 19 as ten ones and some more ones. Decompose 10 into pairs such as (1 9), (2 8),

(3 7) and find the number that makes 10 when added to a given number such as 3

First – Number and Operations Base Ten In first grade, students learn to view ten ones

as a unit called a ten. Compose and decompose this unit flexibly. View numbers 11 to 19 as composed of one

ten and some ones allows development of efficient, general base-ten methods for addition and subtraction.

Students see a two-digit numeral as representing some tens and they add and subtract using this understanding.

First – Number and Operations in Base Ten

Second – Number and Operations in Base Ten At Grade 2, students extend their base-

ten understanding to hundreds: Add and subtract within 1000, with

composing and decomposing, and they understand and explain the reasoning of the processes they use. They become fluent with addition and subtraction within 100.

Second – Number and Operations in Base Ten

Third – Number and Operations in Base Ten At Grade 3, the major focus is

multiplication, with addition and subtraction is limited to maintenance of fluency within 1000 for some students and building fluency to within 1000 for others.

Third – Number and Operations in Base Ten

Fourth – Number and Operations in Base Ten At Grade 4, students extend their work

in the base-ten system. Use standard algorithms to fluently add

and subtract. Use methods based on place value and

properties of operations supported by suitable representations to multiply and divide with multi-digit numbers.

Fourth – Number and Operations in Base Ten

Fifth – Number and Operations in Base Ten In Grade 5, students extend their

understanding of the base-ten system to decimals to the thousandths place, building on their Grade 4 work with tenths and hundredths.

Become fluent with the standard multiplication algorithm with multi-digit whole numbers.

Reason about dividing whole numbers with two-digit divisors, and

Reason about adding, subtracting, multiplying, and dividing decimals to hundredths.

Fifth – Number and Operations in Base Ten