# Parts of a square

http://illuminations.nctm.org/LessonDetail.aspx?ID=L307

**A lesson plan for grades 3–4 Mathematics**

Students investigate the ways shapes can be divided into equal pieces with one or two cuts. It provides a review of the following vocabulary terms: square, triangle, and rectangle; congruent, one-half, and one-fourth. The other lessons in this unit build on this introductory lesson. Illuminations provides helpful activity sheets and resources and detailed directions for completing the lesson.

Students will:

- Explore ways to divide a square into two equal parts with a single cut.
- Explore ways to divide a square into four equal parts.
- Use geometric and fractional terms to name the parts.

NCTM Standards and Expectations:

- Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
- Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
- Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

- Common Core State Standards
- Mathematics (2010)
#### Grade 3

- Number & Operations—Fractions
- 3.NOF.1Understand 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.NOF.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent...

- Number & Operations—Fractions
#### Grade 4

- Number & Operations—Fractions
- 4.NOF.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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...

- Number & Operations—Fractions

## North Carolina Curriculum Alignment

### Mathematics (2004)

#### Grade 3

**Goal 1**: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.**Objective 1.05**: Use area or region models and set models of fractions to explore part-whole relationships.- Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).
- Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.
- Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.
- Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.
- Understand and use mixed numbers and their equivalent fraction forms.

#### Grade 4

**Goal 1**: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.**Objective 1.03**: Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers.