4.2_v3
0 General Document comments
0 Sentence and Paragraph comments
0 Image and Video comments
|
Building Blocks of a Standard
|
|
|
|
| Building Blocks of a Standard | Notes |
| Understand that fractions are equal if they are the same size in an area model or if fractions label the same point on a number line. |
Last year’s standard: 3.NF.3a
(Potential challenge) Students may incorrectly identify the unit (whole) on a number line as the entire portion of the number line in the diagram. For example, when representing ¾, students may incorrectly identify the number 3 on a number line labeled from 0 to 4. Encourage them to first use strips of paper, which can be subdivided in a similar way to the number line, to represent fractions. Sample instructional strategy: Ask students to represent various fractions, including several that are equivalent, using area models or the number line. Compare their sizes or positions and discuss why some fractions are the same size or position on the number line (they are equivalent). |
| Recognize and generate simple equivalent fractions and explain why they are equivalent. For example 1/2 = 2/4 because they are the same size when represented using an area model. |
Last year’s standard: 3.NF.3b
Potential challenge: Students may use different sized wholes when drawing area models. Different wholes may lead to incorrect representations/comparisons of the sizes of different fractions. |
| Write whole numbers as fractions and recognize fractions that are equal to whole numbers. |
Last year’s standard: 3.NF.3c.
Note that expressing whole numbers as fractions is a special case of recognizing equivalent fractions. For example, students may notice that the point labeled 2 on the number line may also be labeled by 2/1, 4/2, and so on. Sample instructional strategy: Ask students to express 2 as a fraction, and compare the different ways they write it (2/1, 4/2, 8/4, and so on). Then repeat the process for 1, which is a more important value for students to understand fluently. |
| Display a fraction as a shaded portion on an area model, or as a point on the number line, and partition each unit fraction part into smaller equivalent parts. Recognize that this does not change the shaded portion of the area model, or the position on the number line, and thus does not change the value of the fractions. | (Potential challenge) Students may struggle to understand that they may further partition a representation of a fraction as long as they partition all of the parts in the representation, and as long as all of the smaller parts are equal. |
| Understand how multiplying the numerator and denominator of a fraction by the same number corresponds to the fraction representation on the number line or area model (partitioning each unit fraction piece into smaller pieces). |
Note that multiplying the numerator and denominator by the same number, n, can be represented on an area model by partitioning the whole into n times as many pieces, leading to n times as many unit fraction pieces as in the original representation of the fraction.
Sample instructional strategy: Ask students to represent a fraction using an area model or the number line. Then encourage them to use that same diagram to represent an equivalent fraction that could be created by multiplying the numerator and denominator of the original fraction by the same number. Discuss student strategies and support students to notice how the multiplier is used in each strategy and each representation. |
| Find equivalent fractions by multiplying the numerator and denominator of a fraction by the same number. | Note that when students understand that multiplying the numerator and denominator of a fraction by the same number generates an equivalent fraction, they are laying a conceptual foundation for fraction multiplication, which they will encounter next year. In particular, generating equivalent fractions in this way is closely related to the mnemonic “multiplying by 1.” Some students (who have a firm understanding of the visual representations of equivalent fractions) may be ready to begin thinking symbolically like this. |
|
Formative Assessment Lesson Plan:
Equivalent Fractions Lesson, Grade 4
|
Common Core Standard 4.NF.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. |
|
Display a fraction as a shaded portion on an area model, or as a point on the number line, and partition each unit fraction part into smaller equivalent parts. Recognize that this does not change the shaded portion of the area model, or the position on the number line, and thus does not change the value of the fraction. |
| Learning Goal(s) | Success Criteria |
|
|
| Misconceptions students are likely to have as they work toward the Goals: |
|
| Strategies to share Learning Goals and Success Criteria with students |
|
| Classroom strategies to elicit evidence |
|
Collecting Evidence: Start of Lesson
|
Collecting Evidence: Middle of Lesson
|
Collecting Evidence: End of Lesson
|
| Key discussion questions I will pose during instruction |
|
Discussion Questions: Start of Lesson
|
Discussion Questions: Middle of Lesson
|
Discussion Questions: End of Lesson
|
| When will I provide descriptive feedback to students? |
|
|
| Strategies for student peer and self-assessment |
|
Peer and Self-Assessment: Start of Lesson Students will receive feedback from their partners as they compare their fraction strips that show thirds and investigate how to create fraction strips for sixths and ninths. |
Peer and Self-Assessment: Middle of Lesson Students will compare their shaded fraction strips as they check their work for the group discussion. |
Peer and Self-Assessment: End of Lesson Students will check their calculations for fractions that are equivalent to three fifths as part of their self-reflection. |
|
General Document Comments 0
icons on the left to see existing comments.
0 archived comments