In this unit, students relate multiplication, particularly their understanding of “times as many” developed throughout 4th grade, to the conversion of measurement units. Students will also solve word problems involving measurement and measurement conversion.
In previous grades, students have worked with many of the metric and customary units (2.MD.1—6, 3.MD.1—2). They’ve noticed the relationship between some units to help them understand various measurement benchmarks but have not yet done any unit conversions. Not only does this unit build on measurement work from previous grades, but it also relies on myriad skills and understanding developed throughout 4th grade. As the Progressions state, “relating units within the metric system is another opportunity to think about place value” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Further, “students also combine competencies from different domains as they solve measurement problems using all four arithmetic operations, addition, subtraction, multiplication, and division” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Lastly, as directly stated in the language of 4.MD.2, students will convert units and solve problems involving fraction and decimal numbers. Thus, while the unit focuses on supporting cluster standards, their instruction enhances much of the major work of the grade, including place value (4.NBT.A), arithmetic operations (4.NBT.B), word problems (4.OA.A), and fractions (including decimal fractions) (4.NF).
As NCTM’s position statement on metric measurement states, “[s]tudents need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships" (The Metric System, NCTM). Thus, students will explore both metric and customary systems of measurement, starting with unit conversions from larger to smaller metric units in Topic A, and then similarly with customary units in Topic B. Then, in Topic C, students deal with more complex cases of fractional and decimal unit conversions. At the end of each topic, students apply their new learning in the context of solving multi-step word problems involving unit conversions.
The unit provides rich opportunities for students to engage with the mathematical practice standards. As the Progressions state, “relating units within the traditional system provides an opportunity to engage in mathematical practices, especially ‘look for and make use of structure’ (MP.7) and ‘look for and express regularity in repeated reasoning’ (MP.8)” (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20). Further, when students solve word problems that involve unit conversions, they "may use tape or number line diagrams for solving such problems (MP.1)" (Progressions for the Common Core State Standards in Mathematics, K-5 Geometric Measurement, p. 20).
As mentioned previously, the unit summarizes and applies much of the major work of the grade in the fresh context of measurement. But, the unit not only incorporates some important 4th grade understanding, it also prepares students for work in future grades, including the very direct link to converting from smaller units to larger ones in 5th grade (5.MD.1) and also to ratios and proportions in the middle grades (6.RP.1) as well as many other areas to come.
Pacing: 14 instructional days (12 lessons, 1 flex day, 1 assessment day)