Check Your Readiness

1.

How many centimeters are there in one meter?
How many meters are there in one kilometer?
How many inches are there in one foot?
How many feet are there in one yard?

Answer:

100
1000
12
3

Teaching Notes

Throughout Unit 7.1, students work with length and area in a variety of contexts. Beginning in Lesson 7, students need to know how to convert units fluently and efficiently, and prior to Lesson 7 some students may use approaches that involve unit conversion.

If most students struggle with this item, plan to use this problem to create an anchor chart early in the unit for students to use as they think about appropriate scales to use throughout this unit.

2.

There are 12 inches in 1 foot and 5,280 feet in 1 mile. Elena ran $2 \frac{1}{2}$ miles.

How many feet did Elena run?
How many inches did Elena run?

Answer:

$13{,}200$ ( $2 \frac{1}{2} \boldcdot 5{,}280=13{,}200$ )
$158{,}400$ ( $12 \boldcdot 13{,}200=158{,}400$ )

Teaching Notes

Students perform multiple unit conversions, working with fractions and large numbers.

If most students struggle with this item, plan to practice unit conversions before doing Lesson 11. In Grade 6 Unit 3 Lessons 3 and 4, you will find activities to support conversions with fractions and large numbers.

3.

Elena drank 3 liters of water yesterday. Jada drank $\frac{3}{4}$ times as much water as Elena drank. Lin drank twice as much water as Jada drank.

Did Jada drink more or less water than Elena drank? Explain how you know.
Did Lin drink more or less water than Elena drank? Explain how you know.

Answer:

Less. $\frac{3}{4} < 1$ , so multiplying by $\frac{3}{4}$ makes a positive number smaller.
More. Doubling $\frac{3}{4}$ of a quantity is the same as multiplying the quantity by $\frac{3}{2}$ , and $\frac 3 2 > 1$ , so the quantity becomes larger.

Teaching Notes

The language of scaling appears in grade 5. While the scaling of this unit is geometric in nature, the language and thought processes associated with this grade 5 standard are very helpful for students.

If most students struggle with this item, plan to emphasize scaling language when launching and synthesizing Lesson 2 Activity 3, "Scaled Triangles." As students are examining the triangles, they will encounter the fractional multipliers 2, $\frac{1}{2}$ , and $\frac{2}{3}$ . MLR2: Collect and Display can be used to highlight student language such as "twice as big" and "half the size" and connect that language to scale factors.

4.

Each small square in the graph paper represents 1 square unit. Find the area of each figure. Explain your reasoning.

Answer:

Figure A has an area of $7\frac{1}{2}$ square units. It can be divided into a 2-unit-by-3-unit rectangle (with an area of 6 square units) and a 1-unit-by-3-unit triangle (with an area of $1\frac{1}{2}$ square units). Figure B has an area of 10 square units. It can be surrounded by a 4-unit-by-4-unit square with two triangles removed. Those triangles have areas of 4 and 2. The area of Figure B is 10 square units because $16 - 4 - 2 = 10$ .

Teaching Notes

One important use of scale models is to help students make calculations about the object represented. Part of these calculations use the scale, and other parts involve finding the lengths or areas of the model. This task makes sure that students can effectively calculate the areas of complex shapes.

If most students struggle with this item, plan to do Lesson 6 Activity 3, "Area of Scaled Parallelograms and Triangles," focusing students on attending to the base and height of their polygon. During the activity launch, include a discussion on how students can determine the area of figures if they aren't sure of a formula. During the launch, review the pre-unit diagnostic item featuring students who decomposed and rearranged figures, as well as students who found parallelograms and triangles and can speak to how they used the base and height. If students need more support with calculating the area of complex shapes, refer to Grade 6 Unit 1.

5.

This rectangle has side lengths $r$ and $s$ .

A rectangle with side lengths labeled r and s.

For each expression, say whether it gives the perimeter of the rectangle, the area of the rectangle, or neither.

$r + s$
$r \boldcdot s$
$2r + 2s$
$r^2 + s^2$

Answer:

Neither (It’s half the perimeter.)
Area
Perimeter
Neither

Teaching Notes

Students have been calculating perimeter and area of figures since elementary school. In grade 6, they begin to use variables and exponential notation in these formulas. This exercise checks students’ understanding of perimeter and area using variables.

If most students struggle with this item, plan to use this problem to review area and perimeter. Grade 6 Unit 1 Lessons 5 and 6 could also be used as review.

6.

A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt. The recipe can be scaled up to make multiple loaves of bread. Complete the table to show the quantities to use for multiple loaves of bread.

number of loaves	cups of flour	tablespoons of water	teaspoons of salt
1	2	12	1
2	4
4		48
	6

Answer:

number of loaves	cups of flour	tablespoons of water	teaspoons of salt
1	2	12	1
2	4	24	2
4	8	48	4
3	6	36	3

Teaching Notes

The content assessed in this problem is first encountered in Lesson 2: Corresponding Parts and Scale Factors.

Students scale figures up and down, which is similar to scaling recipes up and down. This item checks that students are comfortable representing scaling with a table.

If most students struggle with this item, plan to do Lesson 2 Activity 3, Scaled Triangles, with extra attention to Question 3 and the activity synthesis. The synthesis uses the table of scaled copies to help students begin thinking about and articulating scale factor.

7.

Here is a polygon. Draw a scaled copy of the polygon with scale factor 3.

Answer:

Answers vary. Sample response:

<p>Two polygons drawn on a grid. One polygon is a scaled copy of the other polygon.</p>

Teaching Notes

The content assessed in this problem is first encountered in Lesson 1: What are Scaled Copies?.

Some students may have seen or worked with scale drawings before. This item checks whether or not they can reproduce a drawing at a given scale on a grid.

If most students do well with this item, it may be possible to skip Lesson 3 Optional Activity 2.