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The number seventy-five written in standard form is 75 and in expanded form is 70 + 5.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to understand that the value of a digit is impacted by its position in a number. A three in the tens place has a value of 30 while a 3 in the ones place has a value of 3. In Kindergarten, students learned to recognize and count numbers to 100 verbally. Students counted out objects within 20 when given that number verbally or by its written numeral (MTR.5.1).- Instruction includes the understanding that in expanded form each digit of a multi-digit number is assigned a value based on its place.
- Instruction includes experiences with numbers written in different forms (MTR.2.1).
- Instruction includes the use of both proportional and non-proportional models like base ten models or place value disks (MTR.5.1).
Common Misconceptions or Errors
- Students may confuse the value of the digits with how they are stated as a number.
- For example, the standard form of fifteen is 15 and not 51.
- Students may write sequences of numbers rather than expanded form like 83 as 8 + 3 instead of 80 + 3. Having students use base ten blocks to model the number could be helpful for students to understand that the value is directly correlated to tens and ones.
Strategies to Support Tiered Instruction
- Instruction includes opportunities to use a place value chart and base ten blocks to
represent a two-digit number like 76. Students write the expanded form below the base
ten blocks on the place value chart, reading the expanded form aloud. This will assist in
the word form of the numbers. Students write out the word form below the expanded
form, referring to a math word wall where number names may be listed as needed.
- For example, to confirm that students understand the value of the digits ask, “How is the number 67 the same or different than 76?”
- Teacher provides the opportunity to use a place value chart and connecting cubes or
break-apart base ten blocks. Have students represent a two-digit number, like 36. Then,
have the students represent this model with a drawing on the place value chart.
- For example, ask students to use the same blocks and create the representation of 63 (students should not be able to do so with only 3 tens and 6 ones). Discuss why they cannot create this number with blocks they have. Then, provide them more blocks and have them create the representation of 63. Ask them to compare the two different numbers. What do they notice and wonder? Have students identify or match the expanded forms and word forms of the numbers used.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.4.1)
Provide students with the graphic organizer shown below.- Part A. Using tens and ones base ten blocks, create a two-digit number and record in the first column. Write an addition expression in the second column that corresponds to the representation in the first. In the last column, write your number. Repeat until you have created four numbers and written four addition expressions.
- Part B. With a partner, review your work and explain how you know your expressions are correct.
Instructional Items
Instructional Item 1
- How are 16 and 61 alike and different?
Instructional Item 2
- Kourtney wrote a number in expanded form: 90 + 4. What is the standard form of her number?
Instructional Item 3
- Using the word form of a number, complete the table below with the missing standard form or expanded form.
*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 Tutorial
Perspectives Video: Teaching Idea
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will work together to problem solve. The students are presented with a problem in which they have to decide on a procedure for choosing the activity that should be done at a Move-a-Thon fundraiser. Students will organize data in a tally chart as well as a pictograph. In the “twist” students will be given combinations of bills representing the value of each of the activities. Students will work together to reevaluate their original procedure and determine if it should change, along with the rankings.
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
MFAS Formative Assessments
Students are shown the numbers 0 - 20 nonsequentially and asked to read each number aloud.
Original Student Tutorials Mathematics - Grades K-5
Astronaut Archimedes launches into space to teach the outside world all about place value and expanded form in this interactive tutorial.
Student Resources
Original Student Tutorial
Astronaut Archimedes launches into space to teach the outside world all about place value and expanded form in this interactive tutorial.
Type: Original Student Tutorial
Parent Resources
Problem-Solving Tasks
This game can be useful to help students who are having trouble with reversing numerals when reading numbers, for example, 14 as 41 or vise versa. Students often make this mistake because of the difference between reading teens which are read from right to left "Fourteen" versus "forty-one" which is read from left to right.
Type: Problem-Solving Task
This activity provides a connection between the counting sequence and an experience from students' daily lives. It helps to give the students a sense of how "many" each number is. This task also reinforces many skills related to understanding and representing numbers, such as using tally marks, the word form, expanded form, and place value.
Type: Problem-Solving Task
