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• 1 of 21 3.MATH.APT.Unit 4

Rigorous Curriculum Design Engaging Learning Experiences Planner

Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration of Unit 5 Weeks

Engaging Scenario Directions: Incorporate the five elements of effective scenarios: current situation; student challenge; student role; intended audience; product or performance.

The third grade classes are beginning a unit on basketball. We will need to use fractions to compare and find equivalent shooters. Over the next few weeks we will be making fractions and using fractions in games.

Priority Standards 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONING about their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the same whole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions, e.g., by USING a visual fractions model.

Supporting Standards 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. 3.NF.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.NF.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize that equivalencies are only valid when the two fractions refer to the same whole. 3.NF.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. 3.NF.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Geometry 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

• 2 of 21 3.MATH.APT.Unit 4

Interdisciplinary Connections Writing

“Unwrapped” Concepts (students need to know)

“Unwrapped” Skills (students need to be able to do)

DOK Levels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

JUSTIFY 3.NF.3.b

USING 3.NF.3.b

Fraction as a number on a number line 3.NF.2

Fractions on a number line diagram 3.NF.2

 two fractions with same numerator or the same denominator 3.NF.3.b

 that comparisons are valid only when the two fractions refer to the same whole 3.NF.3.b

 the results of comparisons with the symbols >, =, or < 3.NF.3.b

 the conclusions 3.NF.3.b

 a visual fraction model 3.NF.3.b

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• 3 of 21 3.MATH.APT.Unit 4

Corresponding Big Ideas Essential Questions Fractional parts are equal shares of a whole or a whole set. 3.NF.2

Using a visual fraction model will allow you to compare fractions. 3.NF.3.b

Charts, tables, line plot graphs, pictographs, Venn Diagrams, and bar graphs may be used to display data and solve problems. 3.MD.3

The scale increments used when making a bar graph is determined by the scale intervals being graphed. 3.MD.3

How could fractions be represented on a number between 0 and 1? Explain your reasoning. 3.NF.2

How can I fold paper strips to locate fractions on a number line? 3.NF.2

How do you determine which fraction is larger or smaller when they have like numerators or denominators? 3.NF.3.b

How can you use data to create a graph to solve problems? 3.MD.3

How would you decide what increments to use when creating a graph?3.MD.3

Unit Vocabulary Terms “Unwrapped” Priority Standards Concepts Supporting Standards Concepts and

Other Unit-Specific Terms Understand Compare Reasoning Recognizing Record Justify Using Draw Solve

Represent Recognize Explain Generate Express

Performance Task Synopses **You can switch tasks 2 and 3 depending on how you are teaching fractions in your classroom.

Task 1: Create a section fraction bars/strips. Use them to compare fractions with different numerators or denominators. Optional game

Task 2: With a partner, students will shoot 10 baskets (denominator of 10). Students will track baskets made and compare them on a number line. They will then compare using symbols and justify their answers.

Task 3: Students will pick a card that will represent the number of baskets they will shoot (denominators of 12, 7, 5, 9) The number of baskets will determine their group. Students will track baskets made and compare them on a number line within their group. They will then compare using symbols, justify their answers, and share with the class. (Teacher will prepare index cards with the denominators to determine groups. Teacher can choose the denominators.)

• 4 of 21 3.MATH.APT.Unit 4

Performance Task # 1 In Detail

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONING about their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the same whole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions, e.g., by USING a visual fractions model.

3.MD.3 Draw scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each spare in the bar graph might represent 5 pets.

Q: What essential Question(s) and corresponding Big Idea(s) will this task target?

How could fractions be represented on a number between 0 and 1? Explain your reasoning. – Fractional parts are equal shares of a whole or a whole set. How can I fold paper strips to locate fractions on a number line? Using a visual fraction model will allow you to compare fractions. How do you determine which fraction is larger or smaller when they have like numerators or denominators? See above How can you use data to create a graph to solve problems? Charts tables, line plot graphs, pictographs, Venn Diagrams, and bar graphs may be used to display data and solve problems. How would you decide what increments to use when creating a graph? The scale increments used when making a bar graph is determined by the scale intervals being graphed.

U: Which “unwrapped” specific concepts and skills will this task target? “Unwrapped” Concepts (students need to know)

“Unwrapped” Skills (students need to be able to do)

DOK Levels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

Fraction as a number on a number line 3.NF.2

Fractions on a number line diagram 3.NF.2

 two fractions with same numerator or the same denominator 3.NF.3.b

 that comparisons are valid only when the two fractions refer to the same whole 3.NF.3.b

 the results of comparisons with the symbols >, =, or < 3.NF.3.b

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• 5 of 21 3.MATH.APT.Unit 4

JUSTIFY 3.NF.3.b

USING 3.NF.3.b

Draw 3.MD.3

Represent 3.MD.3

Solve 3.MD.3

Using 3.MD.3

 the conclusions 3.NF.3.b

 a visual fraction model 3.NF.3.b

 Scaled picture graph and bar graph

 Data set with several categories 3.MD.3

 One-and two-step “how many more” and “how many less” problems 3.MD.3

 Information presented in scaled bar graphs.3.MD.3

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A: How will the students apply the

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