Middle School Liaison Meeting

January, 2015Presenter: Simi Minhas

CFN 204

Problem of the Day

Pick one or both of the problems to answer. Show all your work, and be ready to justify your thinking.

1. Which fraction is closer to 1, 4/5 or 5/4?

2. 4/5 is closer to 1 than 5/4. Using a number line, explain why this is true.

Mathematical Practices

How do these questions address the mathematical practices?What mathematical practices do they address? Explain

Agenda• Review and take a closer look at the

Mathematics Progressions • Coherence, and Rigor• Instructional implications• Scaffolding

Explain their thinking; critique the reasoning of othersDeveloping mathematical argumentsReading and interpreting real-world problemsTechnical language of the discipline

Coherence

• Coherence provides the opportunity for students to make connections between mathematical ideas and across content areas– Connects the learning both within a grade and across grades– Thinking across grades– Each standard is not a new event, but an extension of

previous learning– Allows students to see mathematics as inter-connected ideas

• Mathematics instruction cannot be relegated to merely a checklist of topics to cover, but instead must be centered around a set of interrelated and powerful ideas, rather than a series of disconnected topics

Rigor

• Conceptual Understanding– Involves more than getting the right answer– Access concepts from multiple perspectives

• Transitions from concrete↔pictorial↔language↔abstract

• Procedural Skill and Fluency– Study algorithms as a way to see the structure of mathematics

(organization, patterns, predictability) or apply a variety of appropriate procedure flexibly to solve problems

– Students are expected to achieve speed and accuracy with simple calculations (at specific grade levels)

– Fluent is used in the Standards to mean “efficient and accurate”• Class time and/or homework should be structured for students to practice core

functions such as single-digit multiplications

• Application– Expectation that students apply math and choose the appropriate concept

for application, even when not prompted to do so– Apply math concepts in real-world situations– Mathematical modeling

Curriculum Unit Template• Stage 1: Desired Results

- What students will know, do and understand• Stage 2: Assessment Evidence

- Evidence that will be collected to determine whether or not desired results are achieved • Stage 3: Learning Plan

- Design learning activities to align with Stage 1 and 2 expectations

- What activities and instruction will engage students and help them better grasp the essence and the value of this topic/content?

Common Core State Standards K-12 Mathematics Progression of Domains

Progressions

Because progressions are so important in the Standards, suggestions for places to begin are not a laundry list of topics but rather a menu of progressions. Experts recommend organizing implementation work according to progressions because the instructional approach to any given topic should be informed by its place in an overall flow of ideas.

Progressions• Counting and Cardinality and Operations and Algebraic

Thinking: grades K–2 • Operations and Algebraic Thinking: multiplication and division

in grades 3–5, tracing the evolving meaning of multiplication, from equal-groups thinking with whole numbers in grade 3 to scaling-oriented thinking with fractions in grade 5.

• Number and Operations—Base Ten: addition and subtraction in grades 1–4

• Number and Operations—Base Ten: multiplication and division in grades 3–6

• Number and Operations—Fractions: fraction addition and subtraction in grades 4–5, including parallel development of fraction equivalence in grades 3–5

Progressions• Number and Operations—Fractions: fraction multiplication

and division in grades 4–6 • The Number System: grades 6–7 • Expressions and Equations: grades 6–8, including how this

extends prior work in arithmetic • Ratio and Proportional Reasoning: its development in grades

6–7, its relationship to functional thinking in grades 6–8, and its connection to lines and linear equations in grade 8

• Geometry: work with the coordinate plane in grades 5–8, including connections to ratio, proportion, algebra and functions in grades 6–HS

• Geometry: congruence and similarity of figures in grades 8–HS, with emphasis on real-world and mathematical problems involving scales and connections to ratio and proportion

Progressions• Modeling with equations and inequalities in high school,

development from simple modeling tasks such as word problems to richer more open-ended modeling tasks

• Seeing Structure in Expressions, from expressions appropriate to 8th–9th grade to expressions appropriate to 10th–11th grade

• Statistics and Probability: comparing populations and drawing inferences in grades 6–HS.

• Additionally, one of the important ―invisible themes in the Standards involves units as a cross-cutting theme in the areas of measurement, geometric measurement, base-ten arithmetic, unit fractions, and fraction arithmetic, including the role of the number line.

What are Learning Progressions?A learning progression is not a list• Learning progressions reflect:– levels of thinking– big ideas– topics• Learning progressions also reflect on:– mathematical processes– mathematical practices– attitudes

Why Learning Progressions?

• Mathematical development– end in mind– sequential and hierarchical– certain concepts and skills must be learnedbefore others• Expectations– appropriate level behavior– behaviors from the previous and next levels

Using Progressions to Inform Instruction

• How could learning progressions influence instruction?

• What are some things that you had to attend to?• What are some ways that we can differentiate

instruction?• What are the implications for planning for

instruction?• How might you assess student understanding

specifically related to ELLs and SWDs?

Questions to consider

• What are some things that you had to attend to?• What are some things that ELLs need to be aware

of?• What are the implications for planning for

instruction?• How might you assess student understanding

specifically related to ELLs?• What are the implications for professional

development?

Important Links

• http://www.edinformatics.com/testing/ny.htm

• https://www.engageny.org/resource/test-guides-for-english-language-arts-and-mathematics

• https://www.engageny.org/resource/new-york-state-common-core-sample-questions

NYS Assessments

How can we use the information provided in the Educator’s Guide to inform our instruction?

What test sophistication plan do you have?

Questions and Feedback

• Questions • Concerns• Next steps• Feedback: Please fill out the feedback forms