Standard #: MA.4.M.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.4.M.1.1

Terms from the K-12 Glossary

• NA

Vertical Alignment

Previous Benchmarks

• MA.3.M.1.1

Next Benchmarks

• MA.5.M.1.1

Purpose and Instructional Strategies

The purpose of this benchmark is for students to see the relationships between the units they use for measurement. Students should begin to generalize that the smaller the unit is, the more precise measurement they will get, but will also need more of the unit to measure (MTR.5.1). Work in this benchmark builds from grade 3 foundations of using customary measurements (MA.3.M.1.1).

• For instruction, students need to use measuring devices in class to develop a sense of the attributes being measured to have a better understanding of the relationships between units. 
• The number of units relates to the size of the unit. Students need to develop an understanding that there are 12 inches in 1 foot and 3 feet in 1 yard. Allow students to use rulers or a yardstick to discover these relationships among units of measurements. Using 12-inch rulers and yardsticks, students will see that three of the 12-inch rulers are the same length as a yardstick, so 3 feet is equivalent to one yard. A similar strategy can be used with rulers marked with centimeters and a meter stick to discover the relationships between centimeters and meters.
• To help students to visualize the size of units, they should be given multiple opportunities to measure the same object with different measuring tools. 
  • For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yardsticks. Students should notice that it takes fewer yard sticks to measure the room than rulers or tiles and explain their reasoning. 
• During instruction, have students record measurement relationships in a two-column table or t-chart. 
• Students are not expected to memorize conversions. Students should be provided conversion tools (e.g., charts) during instruction.

Common Misconceptions or Errors

• Students can assume that converting from smaller units to larger units (e.g., ounces to pounds), that multiplication is used, and when converting from larger units to smaller units (e.g., pounds to ounces), that division is used. To assist students with this misconception, expect them to estimate reasonable solutions.

Strategies to Support Tiered Instruction

• Instruction includes demonstrating which operation to use when converting from smaller units to larger units (e.g., ounces to pounds) and when converting from larger units to smaller units (e.g., pounds to ounces). Instruction also includes estimating reasonable solutions. The teacher models a think aloud and records the relationships on a two- column chart. 
• For example, “If a ribbon is 11 yards 2 feet in length, how long is the ribbon in feet?” 
• “I know that for every 1 yard, there are 3 feet. So, I can multiply the number of yards by 3 to convert to feet. I also know that for every 3 feet, there is one yard. I can divide the number of feet by 3 to convert to yards. Therefore 2 yards convert to 6 feet and 6 feet converts to 2 yards. To find out how many feet there are in 11 yards, 2 feet, I have to multiply the number of yards by 3. 11 yards × 3 = 33 feet. Next, I have to add the extra 2 feet. So, 11 yards, 2 feet converts to 35 feet.” 

• Instruction includes using a bar model or tape diagram to show the relationship between the units. The teacher models a think aloud. o For example, “If a ribbon is 11 yards 2 feet in length, how long is the ribbon in feet?”
  • “I know that for every 1 yard, there are 3 feet. So, I can multiply the number of yards by 3 to convert to feet. I also know that for every 3 feet, there is one yard. I can divide the number of feet by 3 to convert to yards. Therefore 2 yards convert to 6 feet and 6 feet converts to 2 yards. To find out how many feet there are in 11 yards, 2 feet, I have to multiply the number of yards by 3. 11 × 3 = 33. Next, I have to add the extra 2 feet. So, 11 yards, 2 feet converts to 35 feet.”

Instructional Tasks

Instructional Task 1 (MTR.3.1) 

Calculate how many minutes there are in 1 week.