Students learn about the idea of estimating a measurement in this unit. Students are going to:
- Determine an object's length using nonstandard units.
- Measure to confirm their estimations using nonstandard units.
- How precise must measurements and calculations be?
- How are mathematical properties of things or processes measured, computed, and/or interpreted?
- What does it mean to evaluate or estimate a numerical quantity?
- What qualifies a tool or approach as suitable for a particular task?
- When is it appropriate to compute instead of estimate?
- Why does "how" we measure differ depending on "what" we measure?
- Estimate: To calculate approximately.
- Length: Measurement of an object from end to end.
- Measure: The extent, quantity, amount, or degree of something, as determined by measurement or calculation.
- small paper clips
- large paper clips
- connecting cubes
- pennies or counters and straws (optional)
- pencil
- scissors
- equal lengths of string for small groups
- masking tape
- Measurement Worksheet (M-1-5-2_Measurement Worksheet)
- Lesson 2 Assessment (M-1-5-2_Lesson 2 Assessment)
- You can help evaluate students' proficiency by sharing your observations from the lesson activities and class discussions.
- You can use the Lesson 2 Assessment (M-1-5-2_Lesson 2 Assessment) to evaluate mastery even further.
Explicit instruction, modeling, scaffolding, and active engagement
W: Before measuring, students learn about estimating.
H: Students gain the ability to gauge an object's length and then measure it in a range of nonstandard units.
E: Students use nonstandard units, like paper clips, connecting cubes, or pennies, to measure and estimate objects in the classroom.
R: Gathering together to discuss their estimates and measures, the class goes over what they learned during the activity.
E: Assess students' comprehension through dialogue to ascertain their familiarity with measuring and estimating. Keep an eye on the students throughout the exercise to see if they are measuring with the nonstandard units end to end.
T: Adapting the lesson to the needs of the students is possible. Students can practice and reinforce lesson concepts with a small-group activity that offers a less demanding option. Students can measure the distances between circular objects for a more challenging exercise.
O: Students practice measuring objects in the classroom using a nonstandard unit, like a paper clip.
Note: To ensure that every student has a basic understanding of length and width, go over these terms in class if you haven't already had previous measurement lessons.
"We're going to practice measuring the lengths of objects in our classroom today. To assist us in measuring the length, a range of diverse objects will be used. What might we do?" Accept any logical response. "Let's begin by measuring the length of this book with large paper clips. Let's estimate or guess how many paper clips it will take before we take any measurements. What number of large paper clips do you estimate it will require?" Using a chosen color, write the estimates on the board. "Now that we have our approximations, let's measure to determine the required number of paper clips." To measure the book, arrange the paper clips end to end. Engage students in a discussion about the significance of precisely positioning each new paper clip at the end of the preceding one, without any spaces or overlaps. Using a different color from the estimate, write the actual number of paper clips on the board. "Did our estimation and our measurement match up well?" Discuss with the students how they would improve the estimate if it wasn't close.
"Let's now examine a method that can assist you in estimating more precisely." Connect a row of ten connecting cubes. "We're going to measure the length of my desk using the ten cubes that I have arranged in a row. To help maintain a straight line, I ran a piece of masking tape along the edge. How long do you think the desk will be in cubes? Take a look at this row of ten to assist you." On the board, write the estimates. "Let's check the accuracy of our estimate." To find the true number of cubes, place rods made up of ten cubes along the masking tape. "How accurate was our estimation this time? What makes estimating crucial before measuring?" (Most math in real life is mental calculations and estimations. Students need to have some estimation experience to assess the reasonableness of their responses. Students' number sense strengthens, and their computational fluency and mental math skills are enhanced through estimation practice.) Students should be told that estimates are only guesses and are never wrong. When estimating, however, emphasize the concept of reasonableness.
You'll be working in small groups on an exercise that is similar to this one. Every group will measure and estimate a variety of objects. Use the various colors we've selected for each to record your estimates and actual measurements. Give a small paper clip and the Measurement Worksheet (M-1-5-2_Measurement Worksheet) to each group. Before measuring an object's length with a small paper clip as a nonstandard unit, have students estimate each object's length on the worksheet. Make sure that the students fill out their worksheets with their measurements and estimations. Make sure that students are estimating before measuring by taking a look at their processes.
After the students have completed the worksheet, reconvene the class. With the students, go over the answers. Their real answers should be very similar, even though their estimates might differ. "If you used a larger paper clip, how would your answers change?" Reacting by saying that they would require fewer paper clips is how students should respond. Show how bigger paper clips require fewer overalls so that every student can see them. "If you had used a smaller paper clip, how would your response have changed?" Discuss how using a smaller paper clip requires more paper clips.
Students can return to their seats and finish the Lesson 2 Assessment (M-1-5-2_Lesson 2 Assessment) after they have finished discussing the results. Students must first estimate and then measure the length of two pictures on the assessment using nonstandard units like paper clips, pennies, or cubes.
Extension:
Routine: Ask students to find an object in the classroom that is a certain number of cubes long. Through the use of cubes placed next to the object, students can validate their estimates of length before selecting an object in this exercise.
Small Group: Have students estimate and measure object lengths with connecting cubes. Because the cubes lock together, it is possible to reinforce the idea that the nonstandard units should touch one another from end to end.
Expansion: Ask students, "How can we measure the distance around something?" Show the class a circular object, like an oatmeal container or a large can. Ask a student to measure the distance around the object using cubes. Students ought to understand that accuracy is impossible in this situation. "Is there a better way we could measure around the object?" ask the students. Give the recommendations a try with your students. Using a piece of string to measure the area surrounding the object and then measuring the string with cubes is one possible suggestion. Ask students to measure the distances with strings between various objects in the classroom.
