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### Parts of a Square

3-5

Students investigate the ways shapes can be divided into equal pieces
with one or two cuts. The lesson 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.### Describing Designs

3-5

Students create designs and describe them to a classmate, using fractional and geometric terms. This lesson provides a context for using the following vocabulary terms: horizontal, vertical, square, rectangle, triangle, diagonal, one-half, and one-fourth.### Exploring Flips and Slides

3-5

This lesson builds on the previous two lessons and encourages students to explore the geometric transformations of reflections and translations. Students create a design. Then, using flips and slides, students make a four-part paper "mini-quilt." While the formal terms are *reflection*and

*translation*, the more informal terms

*slide*and

*flip*are used at this stage. The experience focuses students’ attention on the changes these geometric transformations make in a student-designed quilt square.

### Exploring Turns

3-5

This lesson encourages students to explore the geometric transformation
of rotation. Students create a design then, using turns, make a
four‑part paper "mini-quilt" with that design as the basis. While the
formal term is rotation, the more informal turn is used at this grade
band. The experience focuses students’ attention on the changes the
geometric transformations make in a student-designed quilt square.
### Analyzing Designs

3-5

This lesson encourages students to explore the geometric transformation
of rotation, reflection and translation more fully. Students create a
design then, using flips, turns, and slides, make a 4-part paper
"mini-quilt" square with that design as the basis. This experience
focuses students’ attention on both the changes produced by the
geometric transformations and on line symmetry.### Planning and Making a Mini-Quilt

3-5

Students create a quilt using the three transformations and investigate the ways shapes can be colored to show one-half and one-fourth. They locate lines of symmetry and create a set of directions for making their quilt block.### Hopping on the Number Line

3-5

In this lesson, students generate products using the number line model.
This model highlights the measurement aspect of multiplication and is a
distinctly different representation of the operation. The order
(commutative) property of multiplication is also introduced. Students
are encouraged to predict products and to answer puzzles involving
multiplication.### Exploring Equal Sets

3-5

This lesson builds on the previous lesson and encourages students to
explore another model for multiplication, the familiar set model.
Students find products using equal sets and present results in the form
of a table. The students apply their knowledge about multiplication in
the creation of pictographs.### Modeling Multiplication With Streets and Avenues

3-5

This lesson encourages students to explore the array model of
multiplication, a model that lays an important foundation for the later
study of area. The lesson focuses on the factors 4 and 6. Students will
also explore products with 0 or 1 as a factors. First students make
arrays with counters, and then they create a second concrete example of
the array model using toothpicks. They also write problems which
involve multiplication.### Balance Beam Discoveries

3-5

This lesson encourages students to explore another model of
multiplication, the balance beam, and another relationship, the inverse
of multiplication. This exploration leads naturally into representing
multiplication facts in equation form. In addition to extending their
understandings of the concept of multiplication, students begin to
practice the multiplication facts by playing the Product Game.