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Examples
The numbers 3,475; 4,743 and 4,753 can be arranged in ascending order as 3,475; 4,743 and 4,753.Clarifications
Clarification 1: When comparing numbers, instruction includes using an appropriately scaled number line and using place values of the thousands, hundreds, tens and ones digits.Clarification 2: Number lines, scaled by 50s, 100s or 1,000s, must be provided and can be a representation of any range of numbers.
Clarification 3: Within this benchmark, the expectation is to use symbols (<, > or =).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Number Line
- Whole Number
- Equal sign
- Equation
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
- The purpose of this benchmark is for students to compare two numbers by examining the place values of thousands, hundreds, tens and ones in each number. This work extends from the Grade 2 expectation to plot, order and compare up to 1,000 (MA.2.NSO.1.2). Students will expand on this work in Grade 4 when they plot, order and compare multi-digit whole numbers up to 1,000,000 (MA.4.NSO.1.3).
- Instruction should use the terms greater than, less than and equal to, as well as the corresponding symbols (>, <, and =). Students should use place value strategies and scaled number lines (horizontal and vertical) to justify how they compare numbers and explain their reasoning. Instruction should not rely on tricks for determining the direction of the inequality symbols. Students should read entire statements (e.g., read 7,309 > 7,039, “7,309 is greater than 7,039” and vice versa) (MTR.2.1, MTR.3.1).
- Students should understand the meaning of the ≠ symbol through instruction. It is recommended that students use = and ≠ symbols first. Once students have determined that numbers are not equal, then they can determine “how” they are not equal, with the understanding now that the number is either greater than (>) or less than (<). If students cannot determine if amounts are ≠ or = then they will struggle with > or <. This will build understanding of statements of inequality and help students determine differences between inequalities and equations (MTR.6.1).
- Students should practice putting sets of whole numbers with values up to 10,000 in ascending and descending order. For example, have students put the following set of numbers (5,881; 4,367; 6,777 and 1,004) in ascending order (1,004; 4,367; 5,881 and 6,777) or in descending order (6,777; 5,881; 4,367 and 1,004).
Common Misconceptions or Errors
- Often students think of these relational symbols as operational symbols instead. In order to address this misconception, allow students to have practice using the number line and/or place value blocks to see the relationship between one number and the other.
Strategies to Support Tiered Instruction
- Teacher uses a number line, base-ten blocks, place value charts and relational symbols to demonstrate the relationship between one number and the other.
- For example, the teacher uses a number line and relational symbols to compare 487 and 623, labeling the endpoints of the number line 0 and 1,000. The teacher asks students to place 487 and 623 on the number line, discussing the placement of the numbers and distance from zero. Next, the teacher uses the number line to demonstrate that 487 is closer to zero than 623 so 487 < 623 and that 623 is farther from zero so 623 > 487. Then, the teacher explains that 487 and 623 are not the same point on the number line so 487 ≠ 623 and asks students to identify numbers that are greater than... and less than.... Finally, the teacher repeats with two four-digit numbers (number line endpoints of 0 and 10,000) and discusses the placement of the other numbers on the number line and if their values are greater than or less than other numbers.
- For example, the teacher uses base-ten blocks, a place value chart and relational symbols to compare 274 and 312. The teacher begins by having students represent 274 and 312 using base-ten blocks and a place value chart and asking students to compare these numbers, beginning with the greatest place value. Next, the teacher explains that the number 274 has 2 hundreds and the number 312 has 3 hundreds so 274 < 312 and 312 > 274 and that 274 and 312 have different digits in the hundreds place so 274 ≠ 312.
Instructional Tasks
Instructional Task 1 (MTR.3.1, MTR.7.1)
- Plot the numbers 3,790, 3,890, 3,799, 3,809 on the number line below.
Instructional Task 2
- Choose two values from the list and compare them using >, <, or =.
- Choose a number between 3,799 and 3,809 and plot it on the number line.
- Use evidence from your number line to justify which number is greatest.
Instructional Task 3
- The students at Imaginary Elementary School participated in a school-wide Read-a-Thon.
The top reader from each grade level is listed below along with the number of pages they read during the contest.
- Which student read the least pages of books? How do you know?
- Deborah says she read more books than Sam and Anton? Is she correct? Put their three book totals in ascending order to prove if she is correct or not.
Instructional Task 4
- Jacob is playing a game with his friend. He flips over the four number cards above.
- Create four different numbers using each of the number cards above only once. Zero cannot be used in the thousands place.
- Using the number line below, plot the four numbers you created.
- What is the greatest number Jacob could create with the four number cards above?
- The Grade 3 classes were having a competition to see which class could collect the most can tabs. Here are the total can tabs that each class collected.
- Which class collected the most can tabs? Put the number of can tabs in descending order to determine the class winner.
- Compare the number of can tabs collected by Mr. Thompson’s class with the number of can tabs collected in Mr. Robert’s class using >, <, or =.
Instructional Items
Instructional Item 1
- Put the following numbers in order from greatest to least: 2,847; 2,478; 2,748; and 2,487.
a. 2,478; 2,487; 2,748; 2,847
b. 2,478; 2,487; 2,847; 2,748
c. 2,847; 2,748; 2,487; 2,478
d. 2,847; 2,487; 2,748; 2,478
Instructional Item 2
Which of the following correctly compares 6,909 and 6,099?- a. 6,909 < 6,099, because the value of the 9 in the tens place of 6,099 is greater than the value of the 0 in the tens place of 6,909.
- b. 6,909 > 6,099, because the value of the 9 in the tens place of 6,099 is greater than the value of the 0 in the tens place of 6,909.
- c. 6,909 < 6,099, because the value of the 9 in the hundreds place of 6,909 is greater than the value of the 0 in the hundreds place of 6,099.
- d. 6,909 > 6,099, because the value of the 9 in the hundreds place of 6,909 is greater than the value of the 0 in the hundreds place of 6,099.
Instructional Item 3
- Select all the following correct comparisons. a. 8,227 < 3,454
b. 6,742 > 6,231
c. 4,404 = 4,404
d. 3,864 > 5,279
e. 1,835 < 3,901
f. 9,067 < 8,067
Instructional Item 4
- Which point is located at number 1,045 on the number line?
a. Point A
b. Point B
c. Point C
d. Point D
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
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Lesson Plans
Problem-Solving Task
Student Center Activities
Worksheet
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will use data to create a procedure for ranking baseball players and determine which baseball player they think is the best hitter using the procedure.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
Students will compare multi-digit numbers to create a procedure for choosing the best car for Edward Easy to buy for his driving school. They will have to weigh quantitative and qualitative factors to determine the best car to purchase. Students will present their recommendations and the steps to the procedure they created in writing and orally.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will compare different nutritional content of chicken nuggets from many restaurants presented in bar graphs. They will factor in the calories, total fat, and sodium information about the nuggets to create a procedure for ranking the nuggets from healthiest to least healthy.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will determine what two snacks should be placed in the school vending machines because the district is asking for healthier and tastier snacks. Factors to consider are calories, fat, protein, sugar, student comments, and cost.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will create a procedure for ranking pool construction companies based on the number of years in business, customer satisfaction, and available pool dimensions. In a “twist,” students will be given information about discounts available by each company. Students will evaluate their procedure for ranking and change it if necessary.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this MEA, students will rank pets from most family-friendly to least family-friendly by considering data such as purchase price, cost to feed, cleanliness, etc. as well as notes regarding the physical description of the pet. In the twist, students will be given information on additional pets as well as information on cleanliness and life expectancy. Students may need to make trade-offs in regards to cost to adopt, feed, and house along with life expectancy, ease of clean up, etc.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will help the Sweet Donut Shop determine what the newest donut will be. Students are given the cost to make each batch along with the selling price and are asked to determine the profit for each batch. Students create a procedure for ranking the donuts and write a letter explaining the procedure and the ranking. In the “twist” students are provided the starting and finishing times for each batch. They must determine the total amount of time, decide if their procedure should change based on the new information, and write a letter explaining whether the procedure changed and the new ranking of the donuts.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
Student Resources
Problem-Solving Task
It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.
Type: Problem-Solving Task
Worksheet
Parent Resources
Problem-Solving Task
It is common for students to compare multi-digit numbers just by comparing the first digit, then the second digit, and so on. This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.
Type: Problem-Solving Task
Student Center Activities
In this game, students build the greatest or least possible number based on instructions by strategically placing digits as a team. They strengthen place value understanding while incorporating physical activity and teamwork.
FCR-STEM’s Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
In this game, students slide numbered caps strategically onto a place value chart to create the greatest or least number as they practice building and reading numbers to reinforce place value understanding.
FCR-STEM's Count Us In! initiative is designed to support out-of-school providers and parents in fostering math success and enjoyment among K-5 children.
Type: Student Center Activity
