# data[].attributes.attachment_link.readable_text
Math.Practice.MP2

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability todecontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability tocontextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.5.NF.B.4b

Common core State Standards

Math: Math

5: Grade 5

NF: Numbers & Operations--Fractions

B: Apply and extend previous understandings of multiplication and division

4b:
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Download Common Core State Standards (PDF 1.2 MB)

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. Why does Ms. Pittard present students with a variety of solutions?

2. How does critiquing solutions help students develop an understanding of multiplying fractions?

3. What can you learn from Ms. Pittard about engaging all students?

School Details

Pathways Elementary School
2100 Airport Road
Ormond Beach FL 32174

Data Provided By:

Teachers

# data[].attributes.attachment_link.description
Fourth and fifth grade teacher Becky Pittard has students critique four possible solutions to a story problem. Becky gives students individual think time to consider the possible solutions. Students then come back together to discuss the solutions in small groups. Finally, the groups present their work to the entire class.

# data[].attributes.attachment_link.readable_text
Math.Practice.MP2

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability todecontextualize--to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability tocontextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.4.NF.B.4b

Common core State Standards

Math: Math

4: Grade 4

NF: Number & Operations--Fractions

B: Build fractions from unit fractions

4b:
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
<br />
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

Download Common Core State Standards (PDF 1.2 MB)

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first video for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. How did Ms. Spies create opportunities for students to share and learn from others?

2. What did students learn by critiquing the teacher's solutions?

3. How did Ms. Spies help her students further their understanding of multiplication as repeated addition?

School Details

Cypress Creek Elementary School
6100 South Williamson Boulevard
Port Orange FL 32128

Data Provided By:

Teachers

# data[].attributes.attachment_link.description
Fourth grade teacher Amy Spies helps her students develop an understanding of multiplying fractions and whole numbers by presenting them with a story problem to solve. Student discuss their solutions in small groups and then present their strategies to the class. Amy gives students teacher solutions to critique and helps students see the multiplication of fractions as repeated addition.

# data[].attributes.attachment_link.description
Multiple part Grade 1 math lesson built around the Common Core. Starting with Math routines, we watch a complete lesson showing students using multiple strategies to add and subtract numbers.

# data[].attributes.attachment_link.readable_text
Math.3.OA.B.5

Common core State Standards

Math: Math

3: Grade 3

OA: Operations & Algebraic Thinking

B: Understand properties of multiplication and the relationship between multiplication and division

5:
Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Download Common Core State Standards (PDF 1.2 MB)

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

Have questions about subscribing? Click Here to learn more.

Discussion and Supporting Materials

Thought starters

1. How do Mr. Crandall's students learn from each other?

2. Mr. Crandall says it's important to give students time to make sense of their ideas. How does he do that?

3. How does Mr. Crandall give students opportunities to revise their thinking?

School Details

Lakeridge Elementary School
7400 South 115th St
Seattle WA 98178

Data Provided By:

Teachers

# data[].attributes.attachment_link.title
Reasoning About Multiplication & Division

# data[].attributes.attachment_link.description
Third graders in Drew Crandall's class look at patterns in multiples of four and compare strategies for solving a multiplication problem. Students begin by looking for patterns in multiples of four and explaining why the patterns are happening. The class then moves on to solving a multiplication problem using a variety of strategies.

# data[].attributes.attachment_link.description
It's simple to teach students Math and surface area within the new Common Core Standards. Watch as Ms. Noonan teaches her elementary school students about surface area, incorporating the Common Core and some of her own teaching strategies.

# data[].attributes.attachment_link.title
Related Problems: Reasoning About Addition

# data[].attributes.attachment_link.description
Teaching addition to 1st grade students. This lesson, Reasoning About Addition Through Related Problems, allows students to see patterns in equations to start making sense of the problems.

# data[].attributes.attachment_link.title
Teacher & Student Discource Actions (Excerpt from Principles to Actions)