Grade6-1-Check-Your-Readiness-(B)-teacher-guide

Area and Surface Area

Assessment : Check Your Readiness (B)

Problem 1

The content assessed in this problem is first encountered in Lesson 1: Tiling the Plane.

This item assesses how students approach finding the area of a rectangle with whole-number side
lengths. The purpose of including tick marks is to give assistance to students who wish to draw a
grid of unit squares. Responses that show drawings with the incorrect number of unit squares,
irregular rows, or irregular columns may indicate that students have not yet learned to structure
two dimensional space, that is, to see a rectangle with whole-number side lengths as composed of
unit squares, or composed of iterated rows or columns of unit squares.

If most students struggle with this item, plan to use the activities in Lesson 1 to support their
understanding of area. The Practice Problems in Lesson 1 can be used for extra practice in
calculating area. In Lesson 2 they will calculate area as they decompose and rearrange shapes to
find area. Plan to emphasize tiling and square units in the warm-up of Lesson 2 if students struggle
to make sense of tiling the rectangle with 30 squares to find its area.

Statement

The rectangle has sides measuring 7 cm and 4 cm. What is the area of this rectangle? Explain
your reasoning.

Solution

28 square centimeters. Possible strategies:

Use a formula like

Draw and count unit squares.

Think in terms of tiling, but multiply to find the area.

•

•

•

Aligned Standards

3.MD.C.6, 3.MD.C.7.a, 3.MD.C.7.b, 4.MD.A.3
Problem 2

The content assessed in this problem is first encountered in Lesson 2: Finding Area by
Decomposing and Rearranging.

This problem assesses two different prerequisite skills. To reason about the area of the shape,
students will need to decompose the shape into two rectangles. Interpreting the expressions in the
answer choices may also pose a challenge for some students. Note that choices C and E represent
two different methods: surrounding with a larger rectangle and decomposing into smaller
rectangles, respectively. It is worth discussing these two techniques with a class, particularly if many
students selected only one of the two methods.

If most students struggle with this item, plan to use a few examples of decomposing rectangles to
find area to begin this lesson. The Practice Problems in Lesson 1 can be used for this. Students will
also get many opportunities in the first several lessons of this unit to decompose shapes and
compare different ways to decompose the same shape.

Statement

Select all the expressions that give the area of
the figure in square units.

A.

B.

C.

D.

E.

Solution

["C", "E"]

Aligned Standards

3.MD.C.7.d, 5.OA.A.2
Problem 3

The content assessed in this problem is first encountered in Lesson 9: Formula for the Area of a
Triangle.

This problem requires students to calculate the area of a rectangle with sides that do not fit nicely
in a lattice grid. In fifth grade, students learned to calculate the area of a rectangle by multiplying
fractional side lengths. Watch for students who are having trouble estimating fractional units
visually.

If most students struggle with this item, plan to use this problem to draw out and support any
misconceptions during the synthesis of Lesson 2 Activity 1.

Statement

Each small square in the graph paper represents 1 square
unit.

Which expression is closest to the area of the shaded
rectangle, in square units?

A.

B.

C.

D.

Solution

C
Aligned Standards

5.NF.B.4.b
Problem 4

The content assessed in this problem is first encountered in Lesson 4: Parallelograms.

Students will need to be comfortable recognizing parallel lines before beginning their work with
parallelograms later in the unit. Some students may correctly select b, but not notice g since that
line is farther away.

If most students struggle with this item, plan to start with Lesson 4 Activity 1 Launch with an
emphasis on defining the term parallel.

Statement

Select all the line segments that appear to be parallel to

.

A.

B.

C.

D.

E.

F.

Solution

["B", "F"]
Aligned Standards

4.G.A.1
Problem 5

The content assessed in this problem is first encountered in Lesson 5: Bases and Heights of
Parallelograms.

In this unit, students will find the area of parallelograms and triangles by decomposing them into
shapes with perpendicular sides and rearranging the pieces. Students will need to be familiar with
perpendicular lines in order to make sense of the “height” of a parallelogram or triangle.

Statement

Select all the figures that have sides that appear to be perpendicular.

A.

B.

C.

D.

E.

Solution

["A", "B"]
Aligned Standards

4.G.A.2
Problem 6

The content assessed in this problem is first encountered in Lesson 17: Squares and Cubes.

Exponential notation is introduced in Lesson 17 of this unit, in the context of calculating surface
area and volume of cubes. Students may have prior knowledge of exponents from their work with
place value in fifth grade.

Statement

Select all the expressions that are equal to

.

A. 10,000

B. 4,000

C.

D.

E.

F. 1,000

G. 40

Solution

["A", "E"]
Aligned Standards

5.NBT.A.2
Problem 7

The content assessed in this problem is first encountered in Lesson 3: Reasoning to Find Area.

This problem assesses whether students understand the term “right triangle.” This problem will also
reveal whether students can picture a 90 degree angle.

Statement

Select all triangles that appear to be a right triangle.

A.

B.

C.

D.

E.

F.

Solution

["A", "C", "F"]
Aligned Standards

4.G.A.2