Illustrative Mathematics
Reasoning about Multiplication and Division and Place Value, Part 2
The learner puts reasoning and estimation to work. The directions are to place a decimal in the answer to make the equation true. Pupils are to look at the two problems, one multiplication and one division, and estimate an answer. No...
Illustrative Mathematics
Reasoning about Multiplication and Division and Place Value, Part 1
Help your class make sense of quantities and their relationships. Given is the product of two numbers. It is up to your number crunchers to think about the quantitative relationship when the product is one-tenth or ten times the product...
Illustrative Mathematics
Harvesting the Fields
This problem involving rates may look simple at first, but it is actually quite challenging. Two different sized fields are harvested by a team of workers and learners must use different rates to calculate the number of workers on the...
NTTI
If You Hopped Like a Frog
Get your frogs hopping by introducing them to the concepts of ratio and proportion. As a class, they perform arithmetic operations using ratios then discover how they represent quantitative relationships. In groups, they write their own...
California Education Partners
Linflower Seeds
How does your garden grow? Use proportions to help Tim answer that question. By using their understanding of proportional relationships, pupils determine the number of seeds that will sprout. They create their own linear relationships...
Mathematics Assessment Project
Comparing Strategies for Proportion Problems
Having problems with proportions? Then solve these proportion problems with an exercise that asks learners to first individually solve a set of problems involving ratios and proportional reasoning. Groups then discuss provided sample...
Achieve
Greenhouse Management
Who knew running a greenhouse required so much math? Amaze future mathematicians and farmers with the amount of unit conversions, ratio and proportional reasoning, and geometric applications involved by having them complete the...
Curated OER
Dental Impressions
What an impressive task it is to make dental impressions! Pupils learn how dentists use proportional reasoning, unit conversions, and systems of equations to estimate the materials needed to make stone models of dental impressions....
Curated OER
Algebra I: Linear Functions
Using rates from a rental car company, young mathematicians graph data, explore linear relationships, and discuss the role of slope and the y-intercept. This lesson allows for the discussion of independent and dependent variables, as...
California Education Partners
Photos
Why do all sizes of pictures not show the same thing? Class members analyze aspect ratios of various sizes of photos. They determine which sizes have equivalent ratios and figure out why some pictures need to be cropped to fit particular...
Education Development Center
Absolute Value Reasoning
Teach solving absolute value inequalities through inquiry. Groups use their knowledge of absolute value and solving inequalities to find a solution set to an absolute value inequality. Working collaboratively encourages discussion,...
NASA
Earth’s Energy Budget - Seasonal Cycles
Earth's energy budget should be in the red. Young researchers review satellite data in a presentation to study Earth's solar radiation. They make both qualitative and quantitative observations about variations in available seasonal...
Mathematics Assessment Project
Sharing Costs Equitably: Traveling to School
Drive or take the school bus? Class members determine the amount each student would have to pay in a carpool situation. They then evaluate the cost in a set of provided examples. I think I'd rather take the school bus!
Curated OER
Let the Rain Come Down!
Second graders construct a bar graph comparing local precipitation to that of the Yucatan. In this graphing lesson, 2nd graders will use conversions and problem solving strategies.
Mathematics Assessment Project
Calculating Volumes of Compound Objects
After determining the volume of various drinking glasses , class members evaluate sample responses to the same task to identify errors in reasoning.
Curated OER
World War II - War Comes to Hawaii
Ninth graders use geographic representations to organize, analyze, and present information on people, places, and environments. They use tools and methods of geographers to construct, interpret, and evaluate qualitative and quantitative...
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
Achieve
Corn and Oats
How much land does a parcel hold? How much fertilizer does it take for a field of corn? Pupils answer these questions and more as they apply ratio reasoning and unit analysis.
Kenan Fellows
Let's Move
Find a statistical reason for a fresh start. Using a hypothetical scenario, individuals research statistical data of three different cities. Their goal? Find the best statistical reason for a business to move to a new location. Their...
Kenan Fellows
Reaction Stoichiometry—How Can We Make Chalk?
What is a reasonable percent yield in the manufacturing process? Scholars develop a process for producing chalk in the third lesson of a six-part series. Then, they must determine the theoretical and percent yield. Discussions about...
Curated OER
Bead It!
Fourth graders use colored beads in two problems and explore the use of proportional reasoning as a problem solving method. Working Students, in groups, explain their reasoning strategies orally, and through drawings.
Curated OER
Ordinal Positions in a Sequence
Students study ordinal positions through class reading and discussion, complete an Animal Parade activity sheet and Internet activity to demonstrate knowledge about ordinal positions with 100% accuracy, and play a math computer game.
Inside Mathematics
Coffee
There are many ways to correlate coffee to life, but in this case a worksheet looks at the price of two different sizes of coffee. It requires interpreting a graph with two unknown variables, in this case the price, and solving for those...
Mathematics Assessment Project
Creating Equations
Using equations to model events. The resource contains four items that prompt individuals to write and solve basic equations. They must reason abstractly and quantitatively while attending to precision when solving the problems.