Grade 6

Readiness Check

Check Your Readiness
1.
  1. Write 10⋅10⋅10⋅1010 \boldcdot 10 \boldcdot 10 \boldcdot 10 as a power of 10.
  2. Write 10310^3 as a number.

Answer:

  1. 10410^4
  2. 1,000

Teaching Notes

This 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 2 and the second part before Activity 3.

2.

A giant panda lives in the Washington, D.C. zoo.

  1. What does the point shown tell you about the panda?

    A point plotted in a coordinate plane.
    A point plotted in a coordinate plane with the origin labeled "O." The horizontal axis is labeled “age in months” and the numbers 0 through 120, in increments of 10, are indicated. The vertical axis is labeled “weight in kilograms” and the numbers 0 through 120, in increments of 10, are indicated. The point with coordinates 36 comma 82 is indicated.

  2. Another panda weighs 90 kilograms and is 110 months old. Plot the point that corresponds to this panda in the coordinate plane shown.

Answer:

  1. The panda is 36 months old and weighs 82 kilograms.
  2. The point (110,90)(110, 90) 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 Lesson 16 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.) 

  1. ?+59=82? + 59= 82
  2. 8⋅?=8968 \boldcdot {?} = 896

Answer:

  1. Sample responses:
    • I would subtract 5959 from each side of the equation.
    • I would find what number you have to add to 5959 to get 8282. You can keep adding tens, then ones to get there.
  2. Sample responses:
    • I would divide each side of the equation by 8.
    • I would find what number times 8 is 896, which is how many times 8 goes into 896.

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 81⋅(37+59)81\boldcdot (37 + 59).

A.

81⋅(59+37)81\boldcdot (59 + 37)

B.

(81⋅37)+59(81\boldcdot 37) + 59

C.

(81⋅37)+(81⋅59)(81\boldcdot 37) + (81 \boldcdot 59)

D.

81+(37⋅59)81 + (37 \boldcdot 59)

E.

(37+59)⋅81(37 + 59)\boldcdot 81

Answer: A, C, 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 A, C, and E have the same value as the given expression. Encourage them to use a diagram in their reasoning.

5.

Jada has 56 beads. That is 39 more beads that Han has. This situation is represented by the following tape diagram.

Select all the equations that represent the situation.

Tape diagram. 2 parts labeled question mark, 39. Total, 56.

A.

39+?=5639+{?}=56

B.

56+39=?56+39={?}

C.

56=?+3956={?}+39

D.

56−39=?56-39=?

E.

?−39=56{?}-39=56

Answer: A, C, D

Teaching Notes

Students will use tape diagrams like this one to represent equations, specifically to solve equations of the form x+p=qx+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.

Tape diagram. 4 equal parts labeled, 3, Total, question mark.

A.

4+3=?4+3={?}

B.

3+3+3+3=?3+3+3+3={?}

C.

?=4⋅3{?}=4 \boldcdot 3

D.

?=3⋅ 3⋅ 3⋅3{?}=3 \boldcdot 3 \boldcdot 3 \boldcdot 3

E.

4÷3=?4 \div 3 = {?}

F.

4=?÷34={?} \div 3

Answer: B, C, F

Teaching Notes

Students will use tape diagrams like this one to represent equations, specifically to solve equations of the form px=qpx=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.