Developing Critical Thinking Skills in Mathematics

Oct 13, 2025 by pynkocean.com 129 views

Developing Critical Thinking Skills in Mathematics

Higher order thinking is a crucial aspect of mathematics education that involves applying critical thinking skills to solve complex problems. It requires students to think beyond the basic arithmetic operations and understand the underlying concepts and relationships between numbers. In this article, we will explore how to use place-value blocks and a hundred chart to show the number that is 10 more than 43, and what that number is.

Understanding Place-Value Blocks

Place-value blocks are a visual representation of numbers that help students understand the concept of place value. Each block represents a specific place value, such as ones, tens, and hundreds. By using place-value blocks, students can visualize the value of each digit in a number and understand how to add or subtract numbers.

Using Place-Value Blocks to Show 10 More Than 43

To show the number that is 10 more than 43 using place-value blocks, we can start by representing the number 43 using blocks. We can use 4 blocks to represent the tens place and 3 blocks to represent the ones place.

  4 | 3
  ---------
  4 blocks (tens) | 3 blocks (ones)

Next, we need to add 10 to 43. We can do this by adding 10 blocks to the ones place. Since we already have 3 blocks in the ones place, we can add 10 blocks to make a total of 13 blocks in the ones place.

  4 | 3
  ---------
  4 blocks (tens) | 13 blocks (ones)

However, we need to consider the tens place as well. Since we added 10 blocks to the ones place, we need to add 1 block to the tens place to make a total of 5 blocks in the tens place.

  5 | 3
  ---------
  5 blocks (tens) | 3 blocks (ones)

Therefore, the number that is 10 more than 43 is 53.

Understanding a Hundred Chart

A hundred chart is a visual representation of numbers from 1 to 100 that helps students understand the relationships between numbers. Each row and column of the chart represents a specific range of numbers, making it easier to identify patterns and relationships.

Using a Hundred Chart to Show 10 More Than 43

To show the number that is 10 more than 43 using a hundred chart, we can start by locating the number 43 on the chart. We can see that 43 is located in the 40s row and the 3s column.

  40 41 42 43 44 45 46 47 48 49
  ---------
  30 31 32 33 34 35 36 37 38 39
  ---------
  20 21 22 23 24 25 26 27 28 29
  ---------
  10 11 12 13 14 15 16 17 18 19
  ---------
  0  1  2  3  4  5  6  7  8  9

Next, we need to add 10 to 43. We can do this by moving 10 spaces to the right on the chart. Since we are moving from the 40s row to the 50s row, we need to add 10 to the tens place as well.

  50 51 52 53 54 55 56 57 58 59
  ---------
  40 41 42 43 44 45 46 47 48 49
  ---------
  30 31 32 33 34 35 36 37 38 39
  ---------
  20 21 22 23 24 25 26 27 28 29
  ---------
  10 11 12 13 14 15 16 17 18 19
  ---------
  0  1  2  3  4  5  6  7  8  9

Therefore, the number that is 10 more than 43 is 53.

Conclusion

Higher order thinking is a crucial aspect of mathematics education that involves applying critical thinking skills to solve complex problems. By using place-value blocks and a hundred chart, students can develop their critical thinking skills and understand the underlying concepts and relationships between numbers. In this article, we explored how to use place-value blocks and a hundred chart to show the number that is 10 more than 43, and what that number is.

Key Takeaways

Place-value blocks are a visual representation of numbers that help students understand the concept of place value.
A hundred chart is a visual representation of numbers from 1 to 100 that helps students understand the relationships between numbers.
By using place-value blocks and a hundred chart, students can develop their critical thinking skills and understand the underlying concepts and relationships between numbers.

Developing Critical Thinking Skills in Mathematics

Higher order thinking is a crucial aspect of mathematics education that involves applying critical thinking skills to solve complex problems. In this article, we will explore some frequently asked questions about higher order thinking in mathematics, and provide answers to help you better understand this concept.

Q1: What is higher order thinking in mathematics?

A1: Higher order thinking in mathematics refers to the ability to apply critical thinking skills to solve complex problems. It involves understanding the underlying concepts and relationships between numbers, and using that understanding to make informed decisions and solve problems.

Q2: How can I develop higher order thinking skills in mathematics?

A2: Developing higher order thinking skills in mathematics requires practice and experience. Here are some tips to help you develop these skills:

Practice solving complex problems that require critical thinking.
Use visual aids such as place-value blocks and hundred charts to help you understand the relationships between numbers.
Ask questions and seek help when you need it.
Work with others to solve problems and share ideas.

Q3: What is the difference between higher order thinking and lower order thinking?

A3: Lower order thinking in mathematics refers to the ability to perform basic arithmetic operations such as addition, subtraction, multiplication, and division. Higher order thinking, on the other hand, involves applying critical thinking skills to solve complex problems.

Q4: How can I use place-value blocks to show the number that is 10 more than 43?

A4: To show the number that is 10 more than 43 using place-value blocks, you can start by representing the number 43 using blocks. You can use 4 blocks to represent the tens place and 3 blocks to represent the ones place. Then, you can add 10 blocks to the ones place and 1 block to the tens place to make a total of 5 blocks in the tens place and 13 blocks in the ones place.

Q5: How can I use a hundred chart to show the number that is 10 more than 43?

A5: To show the number that is 10 more than 43 using a hundred chart, you can start by locating the number 43 on the chart. Then, you can move 10 spaces to the right on the chart to find the number that is 10 more than 43.

Q6: What are some real-world applications of higher order thinking in mathematics?

A6: Higher order thinking in mathematics has many real-world applications. For example, it is used in finance to calculate interest rates and investments, in science to analyze data and make predictions, and in engineering to design and build complex systems.

Q7: How can I assess my students' higher order thinking skills in mathematics?

A7: Assessing higher order thinking skills in mathematics requires a combination of formative and summative assessments. Here are some tips to help you assess your students' higher order thinking skills:

Use formative assessments such as quizzes and classwork to monitor students' progress.
Use summative assessments such as unit tests and final exams to evaluate students' understanding of complex concepts.
Use project-based assessments to evaluate students' ability to apply critical thinking skills to real-world problems.

Q8: What are some common misconceptions about higher order thinking in mathematics?

A8: Some common misconceptions about higher order thinking in mathematics include:

Thinking that higher order thinking is only for advanced students.
Thinking that higher order thinking is only for complex problems.
Thinking that higher order thinking is only for abstract concepts.

Q9: How can I integrate higher order thinking into my mathematics curriculum?

A9: Integrating higher order thinking into your mathematics curriculum requires a combination of planning and implementation. Here are some tips to help you integrate higher order thinking into your curriculum:

Plan lessons that require critical thinking and problem-solving.
Use visual aids such as place-value blocks and hundred charts to help students understand complex concepts.
Encourage students to ask questions and seek help when they need it.
Provide opportunities for students to work with others to solve problems and share ideas.

Q10: What are some resources for further learning about higher order thinking in mathematics?

A10: Some resources for further learning about higher order thinking in mathematics include:

National Council of Teachers of Mathematics (NCTM). (2013). Principles to Actions: Ensuring Mathematical Success for All.
Mathematics Education for a Changing World: 75 Years of the National Council of Teachers of Mathematics.
Online resources such as Khan Academy and Mathway.

By understanding the answers to these frequently asked questions, you can better develop your critical thinking skills and apply them to solve complex problems in mathematics.