Mass vs. Volume: Proportions and Density

Est. Class Sessions: 4–5

Mathematical Standards

5.OA.B: Analyze patterns and relationships. (5.OA.B.3)
5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions.(5.NF.A.1)
5.NBT.A: Understand the place value system. (5.NBT.A.1)
5.MD.C: Geometric measurement: understand concepts of volume. (5.MD.C.4)

Standards for Mathematical Practice

MP1.: Make sense of problems and persevere in solving them.
MP2.: Reason quantitatively.
MP3.: Construct viable arguments and critique the reasoning of others.
MP4.: Model with mathematics.
MP5.: Use appropriate tools strategically.
MP6.: Attend to precision.
MP7.: Look for and make use of structure.
MP8.: Look for and express regularity in repeated reasoning.

Students find the mass and volume of different amounts of clay and different-sized steel spheres. They use proportional reasoning to discover that the density of a material does not change when different amounts of a material are measured. Several extension activities are offered following the lesson.

Content in this Lesson

Representing the relationship between variables as a ratio [E2].
Finding equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables) [E3].
Using ratios and proportions to solve problems [E4].
Measuring mass to the nearest tenth of a gram [E6].
Measuring volume by displacement to the nearest tenth of a cc [E7].
Collecting and organizing data into a table and line graph to represent the relationship between variables [E10].
Representing the variables and procedures of an investigation in a drawing [E9].
Making point graphs and drawing best-fit lines to represent ratios and proportional relationships [E11].
Using patterns in tables and line graphs to make predictions and solve problems [E12].
Translating between different representations of ratios (graphic and symbolic).
Knowing the problem [MPE1].
Finding a strategy [MPE2].
Showing work [MPE5].
Using labels [MPE6].

Daily Practice and Problems O–V

O. What Is the Shape

P. Order of Operations

Q. Computation Review

R. Problem Solving with Decimals

S. Volume

T. True Number Sentence

U. Order Decimals

V. Prime Factors

Materials for Students

		Daily Practice and Problems	Lesson	Homework	Assessment
Student Books	Student Guide	All Pages Reference	Mass vs. Volume: Proportions and Density Pages 543–548	Mass vs. Volume: Proportions and Density Homework section Pages 549–550	Mass vs. Volume: Proportions and Density Lab Pages 543–545 Mass vs. Volume: Proportions and Density Check-In: Questions 13–16 Page 546
Teacher Resources	Teacher Guide - digital	DPP Item O DPP Item P DPP Item Q DPP Item R DPP Item S DPP Item T DPP Item U DPP Item V	Three-Column Data Table Centimeter Grid Paper 2 copies per student	Home Practice Part 5	Mass vs. Volume: Proportions and Density Lab Feedback Box Mass vs. Volume: Proportions and Density Check-In: Questions 13–16 Feedback Box

Supplies for Student Pairs

five 1/2-inch-diameter steel spheres

one 1-inch-diameter steel sphere

one 11/4-inch-diameter steel sphere

enough clay to make 3 pieces of about the same size as the steel spheres and a small piece for leveling the balance; (clay cannot be water soluble)

two-pan balance
set of gram masses
250-cc graduated cylinder
100-cc graduated cylinder
paper towels
eyedropper
cup or beaker for pouring water
calculator
ruler
vegetable oil, corn syrup, clear soda, raisins, eggs, salt, and food coloring for the extension, optional

Supplies for Students

Completed Sink and Float Tables from Lesson 3 (Student Activity Book) Page 443
drawing paper
colored pencils, optional

Materials for the Teacher

Display of Three-Column Data Table Master (Teacher Guide)
Display of Centimeter Grid Paper Master (Teacher Guide)
Unit 11 Assessment Record

Assessment in this Lesson

Assessment	Expectation Assessed	Math Practices Expectation Assessed
Mass vs. Volume: Proportions and Density Lab Student Guide Pages 543–545 and the corresponding Feedback Box Teacher Guide - digital	E6. Measure mass to the nearest tenth of a gram. E7. Measure volume by displacement to the nearest tenth of a cc. E9. Represent the variables and procedures of an investigation in a drawing. E10. Collect and organize data into a table and line graph to represent the relationship between variables. E11. Make point graphs and draw best-fit lines to represent ratios and proportional relationships. E12. Use patterns in tables and line graphs to make predictions and solve problems.
Mass vs. Volume: Proportions and Density Check-In: Questions 13–16 Student Guide Page 546 and the corresponding Feedback Box Teacher Guide - digital	E2. Represent the relationship between variables as a ratio. E3. Find equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables). E4. Use ratios and proportions to solve problems. E12. Use patterns in tables and line graphs to make predictions and solve problems.	MPE1. Know the problem. I read the problem carefully. I know the question to answer and what information is important. MPE2. Find a strategy. I choose good tools and an efficient strategy for solving the problem. MPE5. Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking. MPE6. Use labels. I use labels to show what numbers mean.