Lesson Planning and Curriculum Resources Jennifer Young Elementary - - PowerPoint PPT Presentation

Lesson Planning and Curriculum Resources

February 9, 2017

Jennifer Young Elementary Mathematics Supervisor Dawn Caine Mathematics Learning Specialist Kim Bracey

Classroom Teacher, MHES Grade 4

What was NOT changed What was changed

• Instructional standards
• Teacher expectations for

instructional planning

• Available print and electronic

resources

• Order of the instructional

standards

• Structure of the instructional

block (pg. 5)

• Format of the document

2016‐2017 Elementary Mathematics Instructional Organizers

MODULE 8 Suggested Pacing: 15 days

BIG IDEAS

 The meanings of each operation on fractions are the same as the meanings for the operations on whole numbers.  Operations with fractions should begin by applying these same meanings to fractional parts.  For addition and subtraction, it is critical to understand that the numerator tells the number of parts and the denominator the type of part.

RECURSIVE STANDARDS

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown

• quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

INSTRUCTIONAL STANDARDS

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results

• f comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a

visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• 4. NF.B.3b Decompose a fraction into a sum of fractions with the same

denominator in more than one way, recording each decomposition as an

• equation. Justify decompositions, e.g., by using a visual fraction model.

Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8; 2 1/8 = 8/8 + 8/8 + 1/8. 4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem

STANDARDS OF MATHEMATICAL PRACTICE

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of

• thers

4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

MAKING CONNECTIONS

It is imperative at this time that students have the opportunity to use manipulatives to find equivalent fractions as opposed to using a procedure to find an equivalent fraction. Standard 4.NF.3b should be taught similarly to decomposing whole numbers. There is more than one way to decompose a

• fraction. Be sure to use improper fractions as well mixed

numbers. The PARCC Diagnostic 3.NF.A (Develop understanding of fractions as numbers) could be used here prior to this Module as a pre‐ assessment of skill mastery.

MY NOTES

Turn to page 26

MODULE 8 Suggested Pacing: 15 days

BIG IDEAS

 The meanings of each operation on fractions are the same as the meanings for the operations on whole numbers.  Operations with fractions should begin by applying these same meanings to fractional parts.  For addition and subtraction, it is critical to understand that the numerator tells the number of parts and the denominator the type of part.

RECURSIVE STANDARDS

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown

• quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

INSTRUCTIONAL STANDARDS

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results

• f comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a

visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• 4. NF.B.3b Decompose a fraction into a sum of fractions with the same

denominator in more than one way, recording each decomposition as an

• equation. Justify decompositions, e.g., by using a visual fraction model.

Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8; 2 1/8 = 8/8 + 8/8 + 1/8. 4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem

STANDARDS OF MATHEMATICAL PRACTICE

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of

• thers

4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

MAKING CONNECTIONS

It is imperative at this time that students have the opportunity to use manipulatives to find equivalent fractions as opposed to using a procedure to find an equivalent fraction. Standard 4.NF.3b should be taught similarly to decomposing whole numbers. There is more than one way to decompose a

• fraction. Be sure to use improper fractions as well mixed

numbers. The PARCC Diagnostic 3.NF.A (Develop understanding of fractions as numbers) could be used here prior to this Module as a pre‐ assessment of skill mastery.

MY NOTES

MODULE 8 Suggested Pacing: 15 days

BIG IDEAS

 The meanings of each operation on fractions are the same as the meanings for the operations on whole numbers.  Operations with fractions should begin by applying these same meanings to fractional parts.  For addition and subtraction, it is critical to understand that the numerator tells the number of parts and the denominator the type of part.

RECURSIVE STANDARDS

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown

• quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

INSTRUCTIONAL STANDARDS

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results

• f comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a

visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• 4. NF.B.3b Decompose a fraction into a sum of fractions with the same

denominator in more than one way, recording each decomposition as an

• equation. Justify decompositions, e.g., by using a visual fraction model.

Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8; 2 1/8 = 8/8 + 8/8 + 1/8. 4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem

STANDARDS OF MATHEMATICAL PRACTICE

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of

• thers

4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

MAKING CONNECTIONS

It is imperative at this time that students have the opportunity to use manipulatives to find equivalent fractions as opposed to using a procedure to find an equivalent fraction. Standard 4.NF.3b should be taught similarly to decomposing whole numbers. There is more than one way to decompose a

• fraction. Be sure to use improper fractions as well mixed

numbers. The PARCC Diagnostic 3.NF.A (Develop understanding of fractions as numbers) could be used here prior to this Module as a pre‐ assessment of skill mastery.

MY NOTES

MODULE 8 Suggested Pacing: 15 days

BIG IDEAS

 The meanings of each operation on fractions are the same as the meanings for the operations on whole numbers.  Operations with fractions should begin by applying these same meanings to fractional parts.  For addition and subtraction, it is critical to understand that the numerator tells the number of parts and the denominator the type of part.

RECURSIVE STANDARDS

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole‐number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown

• quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

INSTRUCTIONAL STANDARDS

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize the comparisons are valid only when the two fractions refer to the same whole. Record the results

• f comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a

visual fraction model. 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

• 4. NF.B.3b Decompose a fraction into a sum of fractions with the same

denominator in more than one way, recording each decomposition as an

• equation. Justify decompositions, e.g., by using a visual fraction model.

Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8; 2 1/8 = 8/8 + 8/8 + 1/8. 4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem

STANDARDS OF MATHEMATICAL PRACTICE

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of

• thers

4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

MAKING CONNECTIONS

It is imperative at this time that students have the opportunity to use manipulatives to find equivalent fractions as opposed to using a procedure to find an equivalent fraction. Standard 4.NF.3b should be taught similarly to decomposing whole numbers. There is more than one way to decompose a

• fraction. Be sure to use improper fractions as well mixed

numbers. The PARCC Diagnostic 3.NF.A (Develop understanding of fractions as numbers) could be used here prior to this Module as a pre‐ assessment of skill mastery.

MY NOTES