In this unit, students will extend their work with multiplicative comparisons to include using models and equations to represent a variety of problem types that have different unknowns (product, group size, and number of groups). Making sense of the quantities involved will reveal that they are all related to each other by multiplicative comparison. Students will then use their knowledge of place value to round numbers and estimate answers in comparison problems as a way to check their thinking with a different method. Finally, students will use their knowledge of conversions to create equivalent measures so that quantities can be compared.
Key Concepts:
 The meaning of multiplicative comparison does not change depending on the type of problem being solved or the units involved (in measurement problems).
 When rounding to estimate solutions, we make choices about which place to round to depending on units and quantities involved.
 When solving measurement problems, it sometimes makes sense to express measurements given in a larger unit in terms of a smaller unit.
Prior Knowledge Needed:
 Use drawings and equations to solve multiplication problems; (Grade 3, Unit 9; 3.OA.A.3)
 A whole number is a multiple of each of its factors; (Grade 4, Unit 1; 4.OA.B.4)
 Multiplication can be thought of as a comparison, including in the context of place value; (Grade 4, Unit 6; 4.OA.A.1, 4.NBT.A.1)
 Multiplicative comparison can also be used to convert between units of length, mass, volume, and time; (Grade 4, Unit 6; 4.MD.A.1)
Units on the Horizon:
 Solving measurement problems using the four operations (Grade 4, Unit 8)
 Problem solving with whole numbers (Grade 4, Unit 14)
Lessons

Lesson objective: Extend understanding that one of the factors in a multiplication equation tells how many times greater the product is compared to the other factor in order to find any unknown quantity. Students bring prior knowledge of using the relat...

Lesson objective: Find unknowns in different types of multiplicative comparison problems. This lesson helps to build procedural skill with multiplicative comparisons. Tape diagrams are used here because they support conceptualizing a larger amount and a...

Lesson objective: Apply understanding of multiplicative comparisons in different types of problems. This lesson provides an opportunity for students to apply their knowledge and understanding of comparisons to a reallife situation. Students are asked t...

Lesson objective: Understand that numbers can be rounded to any place value. Students bring prior knowledge of rounding based on place value from 3.NBT.A.1. This prior knowledge is extended to rounding to different place values. A conceptual challenge s...

Lesson objective: Round numbers to different place values, depending on the quantities involved, in order to estimate solutions. This lesson helps to build procedural skill with estimation. A number line is used here because it highlights where numbers ...

Lesson objective: Apply criteria for rounding to accurately estimate in context. This lesson provides an opportunity for students to apply their knowledge and understanding of rounding to different place values to a reallife situation. Students are ask...

Lesson objective: Understand that when solving measurement problems, it sometimes makes sense to convert a larger unit to a smaller unit. Students bring prior knowledge of using multiplicative comparison to convert units of length, mass, volume, and tim...

Lesson objective: Convert larger units to smaller units in order to compare quantities. This lesson addresses pints and quarts. This lesson helps to build procedural skill with measurement conversions. A function table is used here because it highlights...

Lesson objective: Convert larger units to smaller units in order to compare quantities. This lessons uses cups, pints, quarts, and gallons. This lesson helps to build procedural skill with measurement conversions. A function table is used here because i...

Lesson objective: Apply understanding of converting measurements in order to compare amounts. This lesson provides an opportunity for students to apply their knowledge and understanding of measurement conversions to a reallife situation. Students are a...