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Standards for Mathematics. Standards for Mathematical Practice Apply across all grade levels Describe habits of mind of a mathematically proficient student Standards for Mathematical Content K-8 standards presented by grade level

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standards for mathematics
Standards for Mathematics

Standards for Mathematical Practice

Apply across all grade levels

Describe habits of mind of a mathematically proficient student

Standards for Mathematical Content

K-8 standards presented by grade level

High school standards presented by topic (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability)

Organized into domains that progress over several grades

Two to four “critical areas” at each grade level

mathematical practices
Mathematical Practices

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.
design and organization
Design and Organization

Critical areas at each grade level

design and organization1
Design and Organization

Grade Level Overviews

ratios and proportional relationships
Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratioof wings to beaks in the bird house at the zoo was 2:1, because forevery 2 wings there was 1 beak.” “For every vote candidate A received,candidate C received nearly three votes.”

2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

Domain, Cluster and Standards

reading the standards
Reading the Standards

Standards define what students should understand and be able to do.

Specific advice is often given about instructional approaches.

The actual language can be dense, and probably requires “unpacking.” K-6 “I Can” statements are available on our website.

slide7

I understand what it means to divide by a fraction, and I can solve word problems that involve division with fractions.

slide9

I can create equivalent fractions by scaling up, and I can show this process using visual fraction models.

high school
High School

The high school standards specify the mathematics that all students should study in order to be college and career ready. Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+), as in this example:

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers).

All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students. Standards with a (+) symbol may also appear in courses intended for all students.

modeling standards
Modeling Standards

Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★).

course topics
Course topics
  • Appendix A shows which standards fit into Algebra I, Algebra II, and Geometry.
major shifts in mathematics
Major Shifts in Mathematics

Working like a mathematician:

  • Problem solving
  • Reasoning (proportional reasoning, geometric reasoning, etc.
  • Creating viable arguments
  • Modeling with mathematics
slide14

Reasoning and Sense-making

In square ABCE shown below, D is the midpoint of CE. Which of the following is the ratio of the area of triangle ADE to the area of triangle ADB?

F. 1:1

G. 1:2

H. 1:3

J. 1:4

K. 1:8

videos of classrooms
Videos of classrooms

From the Inside Mathematics web resource

http://InsideMathematics.org

Properties of Quadrilaterals, Grades 9-10, Tuesday Group Work, Pt. A

major shifts in mathematics1
Major Shifts in Mathematics

Focus and coherence

Focus on key topics at each grade level.

Coherent progressions across grade levels.

Balance of concepts, skills and problem-solving

Content standards require a blend of deep understanding, procedural fluency and application.

Mathematical practices

Foster reasoning and sense-making in mathematics.

focus critical areas
Focus: Critical Areas
  • Mathematics Grade 3
  • In Grade 3, instructional time should focus on four critical areas:
  • developing understanding of multiplication and division and strategies for multiplication and division within 100;
  • developing understanding of fractions, especially unit fractions (fractions with numerator 1);
  • developing understanding of the structure of rectangular arrays and of area; and
  • describing and analyzing two-dimensional shapes.
coherence learning progressions1
Coherence: Learning Progressions

Fractions, Grades 3-6

3rd grade: Develop an understanding of fractions as numbers.

4th grade: Extend understanding of fraction equivalence and ordering.

5th grade: Use equivalent fractions as a strategy to add and subtract fractions.

5th grade: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

6th grade: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

on line learning trajectories
On-line Learning Trajectories

http://turnonccmath.net/

balance of concept skill application
Balance of concept, skill & application

Multiplication, single and multi-digit

Fluently multiply and divide within 100, using strategies… By the end of Grade 3, know from memory all products of one-digit numbers.3.OA.7

Solve two-step word problems using the four operations. 3.OA.8

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies… Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.5

Solve multistep word problems posed with whole numbers, including problems in which remainders must be interpreted. 4.OA.3

Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.5

mathematical practices1
Mathematical Practices

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Marty made two types of cookies. He used 2/3 cup of sugar for one recipe and 1/4 cup of sugar for the other. He only has 1 cup of sugar. Is that enough? Explain your reasoning.

Some people might say that

A) Why might they say this?

B) Do you agree?

C) How would you solve this problem?