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The number two hundred seventy-five thousand eight hundred two written in standard form is 275,802 and in expanded form is 200,000+70,000+5,000+800+2 or (2×100,000)+(7×10,000)+(5×1,000)+(8×100)+(2×1).Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Whole Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to read numbers appropriately and to write numbers in all forms and have flexibility with the different forms. This benchmark builds on the work in grade 3 of reading and writing numbers in multiple ways to 10,000 (MA.3.NSO.1.1).- Students should also have opportunities to explore the idea that 285 could also be 28 tens plus 5 ones or 1 hundred, 18 tens and 5 ones.
- Decomposing numbers flexibly helps students reason through multiplication and division strategies. Multiple representations of the number (MTR.2.1) allow for opportunities to apply the commutative and associative properties. This will allow students to explain their thinking and show their work using place-value strategies and algorithms, in addition to verifying that their answer is reasonable.
Common Misconceptions or Errors
- Students may have misconceptions when translating word form to standard form. Numbers like one thousand often do not cause a problem; however, a number like three thousand four can cause problems for students. Many students will understand the 3,000 and the 4 but then instead of placing the 4 in the ones place, students will write the numbers as they hear them, 30,004, not understanding that this number represents more than 3,004.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to model and write numbers with a zero in various place values. A place value chart and models such as base-ten blocks or place value disks can be used to help students understand that when the digit in a multi-digit whole number is 0, it represents a 0 of that place value. Extend this understanding to include writing numbers in word and expanded form.
- For example, in the number 40,607 there are 0 thousands and 0 tens.
- For example, in the number 1,002, there are 0 hundreds and 0 tens.
Instructional Tasks
Instructional Task 1 (MTR.3.1)
Write each number in standard form and in expanded form.- a. Eight hundred two thousand five hundred fifty
- b. Twenty thousand three
- c. One thousand four hundred fifty
- d. Seven hundred nineteen thousand two hundred forty - eight
- e. Three thousand eighty - one
Instructional Items
Instructional Item 1
Select all the ways to rename the number 2,340.- a. 234 tens
- b. 2,340 ones
- c. 234 thousands
- d. 2 hundreds and 34 ones
- e. 2 thousands and 34 tens
- f. 2 thousands and 34 ones
- g. 2 thousands and 34 hundreds
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Tutorials
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will add, subtract, and compare multi-digit numbers in order to help a new movie production company decide which genre they should make for their first movie.
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 are asked to evaluate several space suit designs and select the best design based on given data. Students work in collaborative groups to develop a procedure for selecting the best design and share their ideas with the rest of the class. A twist is introduced and the groups are challenged to test the validity of their 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. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students are asked to write numbers in both standard form (as base ten numerals) and expanded form.
Students are asked to read aloud several numbers that are greater than one thousand.
Students compare two numbers, one given in word form and the other given in expanded form.
Students will write the number name (word form) of a number when given the base-ten numeral (standard form).
Original Student Tutorials Mathematics - Grades K-5
Read and write multi-digit whole numbers using base-ten numerals and number names using the Base 10 place value system in this interactive tutorial.
Note: this tutorial exceeds the number limits of the benchmark.
Learn how to write numbers using place value in different forms like standard, word, and expanded notation in this interactive tutorial.
Student Resources
Original Student Tutorials
Read and write multi-digit whole numbers using base-ten numerals and number names using the Base 10 place value system in this interactive tutorial.
Note: this tutorial exceeds the number limits of the benchmark.
Type: Original Student Tutorial
Learn how to write numbers using place value in different forms like standard, word, and expanded notation in this interactive tutorial.
Type: Original Student Tutorial
Tutorials
In this tutorial, you will look at regrouping a number by different place values.
Type: Tutorial
In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.
Type: Tutorial
Parent Resources
Tutorial
In this tutorial video from Khan Academy, learn to use an abacus to represent multi-digit numbers. This video will explain how the beads on an abacus can each represent ten times the value of the bead to its right.
Type: Tutorial
