Check Your Readiness

1.

Write $10 \boldcdot 10 \boldcdot 10$ as a power of 10.
Write $10^5$ without an exponent.

Answer:

$10^3$
100,000

Teaching Notes

The problem assesses prior knowledge of exponents used to denote powers of 10, which students worked with in grade 5. In Lesson 12, students will expand on their previous work with exponents.

If most students struggle with this item, review the meaning of “power of 10” from IM Grade 5 Unit 6 and the meaning of “exponent” from IM Grade 6 Unit 1. Plan to revisit the first part of this item after Lesson 12 Activity 1 and the second part before Activity 3.

2.

A store sells blocks of cheese in several different sizes.

The point shown represents one block of cheese. What does the point's location tell you?
Another block of cheese costs $7 and weighs 16 ounces. Plot and label a point to represent this block of cheese.

Answer:

The block of cheese weighs 8 ounces and costs $3.
The point $(16, 7)$ is plotted correctly.

Teaching Notes

In this problem, students graph points in the first quadrant of a coordinate plane and interpret the points in a context. These skills will come up in the final sections of this unit, in which students plot points from given relationships, such as between distance and time, or between area and length.

If most students struggle with this item, plot one pair of values together in the last question of Activity 2. If students struggle with the given intervals in that activity, consider working through the first item in the Practice Problems as a class.

3.

Describe what you would do to find the unknown value in each equation. (You do not have to actually find the unknown value.)

${?} - 15 = 34$
${?} \boldcdot 6 = 672$

Answer:

Sample responses:
- I would add 15 to 34.
- I would find what number I have to add to 15 to get 34. I would add the ones and then the tens.
Sample responses:
- I would divide 672 by 6.
- I would find what number times 6 is 672, which is how many times 6 goes into 672.

Teaching Notes

Students are not expected to know the standard ways to solve these equations, which will be codified in this unit, but some students may have been exposed to this material before. The purpose of this question is to assess where students are in their understanding of algebraic thinking. Students with incorrect or blank answers do not need remediation. They will learn this content in the unit.

4.

Without computing, select all the expressions that have the same value as $74 \boldcdot (29+56)$ .

A.

$74 \boldcdot 29+56$

B.

$74+(29+56)$

C.

$74+(56 \boldcdot 29)$

D.

$(74 \boldcdot 29)+(74 \boldcdot 56)$

E.

$(56+29) \boldcdot 74$

Answer:

D, E

Teaching Notes

This problem assesses understanding of the distributive property of multiplication over addition. It also includes recognizing the commutative property of addition and of multiplication within an expression involving parentheses. In this unit, students will explore the distributive property using both numbers and variables.

If most students struggle with this item, consider revisiting this question at the end of Activity 2 of Lesson 9. Ask students to articulate how someone could know, without computing, that D and E have the same value as the given expression. Encourage them to use a diagram in their reasoning.

5.

Select all the equations represented by this tape diagram.

A.

$25 + {?} = 38$

B.

$38 = {?} + 25$

C.

$38- 25 = {?}$

D.

$38 + 25 = {?}$

E.

${?}−25 = 38$

Answer: A, B, C

Teaching Notes

Students will use tape diagrams like this one to represent equations in the upcoming unit, specifically to solve equations of the form $x+p=q$ .

If most students struggle with this item, provide additional support early on in the unit for students who weren't exposed to the tape diagram representation in earlier grades. This could be requiring particular students to draw a tape diagram when an activity prompt does not require one.

6.

Select all the equations represented by this tape diagram.

A.

$6+6+6+6+6= {?}$

B.

$5+6= {?}$

C.

${?}=6 \boldcdot 5$

D.

${?}=6 \boldcdot 6 \boldcdot 6 \boldcdot 6 \boldcdot 6$

E.

${?} \div 5 = 6$

F.

$5= {?} \div 6$

Answer: A, C, E, F

Teaching Notes

Students will use tape diagrams like this one to represent equations in the upcoming unit, specifically to solve equations of the form $px=q$ .

If most students struggle with this item, provide additional support early on in the unit for students who weren't exposed to the tape diagram representation in earlier grades. This could be requiring particular students to draw a tape diagram when an activity prompt does not require one.