Lesson Planning and Curriculum Resources Jennifer Young Elementary Mathematics Supervisor Dawn Caine Mathematics Learning Specialist Kim Bracey Classroom Teacher, MHES Grade 4 February 9, 2017
2016 ‐ 2017 Elementary Mathematics Instructional Organizers What was NOT changed What was changed Instructional standards Order of the instructional • • standards Teacher expectations for Structure of the instructional • • instructional planning block (pg. 5) Available print and electronic Format of the document • • resources
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. INSTRUCTIONAL STANDARDS STANDARDS OF MATHEMATICAL PRACTICE 4.OA.A.3 Solve multistep word problems posed with whole numbers and 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by 1. Make sense of problems and persevere in solving them problems in which remainders must be interpreted. Represent these using visual fraction models, with attention to how the number and size of the 2. Reason abstractly and quantitatively having whole ‐ number answers using the four operations, including problems using equations with a letter standing for the unknown 3. Construct viable arguments and critique the reasoning of parts differ even though the two fractions themselves are the same size. Use others this principle to recognize and generate equivalent fractions. quantity. Assess the reasonableness of answers using mental 4. Model with mathematics 4.NF.A.2 Compare two fractions with different numerators and different computation and estimation strategies including rounding. 5. Use appropriate tools strategically denominators, e.g., by creating common denominators or numerators, or by 6. Attend to precision comparing to a benchmark fraction such as ½. Recognize the comparisons are 7. Look for and make use of structure valid only when the two fractions refer to the same whole. Record the results 8. Look for and express regularity in repeated reasoning of comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a visual fraction model. MAKING CONNECTIONS 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. It is imperative at this time that students have the opportunity to 4.NF.B.3a Understand addition and subtraction of fractions as joining and use manipulatives to find equivalent fractions as opposed to separating parts referring to the same whole. using a procedure to find an equivalent fraction. 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 Standard 4.NF.3b should be taught similarly to decomposing equation. Justify decompositions, e.g., by using a visual fraction model. RECURSIVE STANDARDS whole numbers. There is more than one way to decompose a 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 = fraction. Be sure to use improper fractions as well mixed 8/8 + 8/8 + 1/8. numbers. 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 The PARCC Diagnostic 3.NF.A (Develop understanding of fractions properties of operations and the relationship between addition and as numbers) could be used here prior to this Module as a pre ‐ subtraction. assessment of skill mastery. 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 MY NOTES fraction models and equations to represent the problem
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. INSTRUCTIONAL STANDARDS STANDARDS OF MATHEMATICAL PRACTICE 4.OA.A.3 Solve multistep word problems posed with whole numbers and 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by 1. Make sense of problems and persevere in solving them problems in which remainders must be interpreted. Represent these using visual fraction models, with attention to how the number and size of the 2. Reason abstractly and quantitatively having whole ‐ number answers using the four operations, including problems using equations with a letter standing for the unknown 3. Construct viable arguments and critique the reasoning of parts differ even though the two fractions themselves are the same size. Use others this principle to recognize and generate equivalent fractions. quantity. Assess the reasonableness of answers using mental 4. Model with mathematics 4.NF.A.2 Compare two fractions with different numerators and different computation and estimation strategies including rounding. 5. Use appropriate tools strategically denominators, e.g., by creating common denominators or numerators, or by 6. Attend to precision comparing to a benchmark fraction such as ½. Recognize the comparisons are 7. Look for and make use of structure valid only when the two fractions refer to the same whole. Record the results 8. Look for and express regularity in repeated reasoning of comparisons with symbols >, =, <, and justify the conclusion, e.g., by using a visual fraction model. MAKING CONNECTIONS 4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. It is imperative at this time that students have the opportunity to 4.NF.B.3a Understand addition and subtraction of fractions as joining and use manipulatives to find equivalent fractions as opposed to separating parts referring to the same whole. using a procedure to find an equivalent fraction. 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 Standard 4.NF.3b should be taught similarly to decomposing equation. Justify decompositions, e.g., by using a visual fraction model. RECURSIVE STANDARDS whole numbers. There is more than one way to decompose a 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 = fraction. Be sure to use improper fractions as well mixed 8/8 + 8/8 + 1/8. numbers. 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 The PARCC Diagnostic 3.NF.A (Develop understanding of fractions properties of operations and the relationship between addition and as numbers) could be used here prior to this Module as a pre ‐ subtraction. assessment of skill mastery. 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 MY NOTES fraction models and equations to represent the problem
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