Place value
What tool do you use to help a student who misunderstands the value of the digits in large numbers
Base-10 blocks, place value charts
A student writes 4567 + 3972 = 714139.
What did the student do to get this result?
Added digits without using considering regrouping
What is a term for believing that a larger denominator means a larger fraction?
a misconception
What is the best strategy of solving this problem 300 – 275
Use compensation instead of regrouping
The reason students may not understand why 24 ÷ 6 = 4 only that they memorized it.
Overemphasis on memorization instead of visual or contextual models
A student writes 4382- 2879 =2517
What challenge is the student revealing?
Subtracts the smaller number from the bigger
A student writes 4567 + 3972 = 714139.
How do you help a student who shows this learning gap in addition?
Teach regrouping using manipulatives
What is the reason for a student to see 3/4 as "3 and 4" instead of 3 parts of 4?
The student sees a fraction as two separate whole numbers rather than a single quantity.
What is the cause of errors in solving problems like 400 – 186 due to difficulty in borrowing across zeros?
Procedural teaching without strong conceptual foundation.
How do you help students who not understand why 24 ÷ 6 = 4?
Use manipulatives for grouping and sharing. Procedural fluency must be preceded by conceptual understanding
How do you help a student who subtracts a digit number from a bigger digit, regardless of the numbers.
Teach regrouping using concrete manipulatives like base ten blocks
What causes struggles with mental math strategies like making tens, doubling, or bridging through 100.
A weak number sense
What is the misconception that 1/3 > 1/2
The misconception is based on whole number thinking because 3 > 2
How do you solve students' challenges or gaps with problems like 400 – 186 due to difficulty in borrowing across zeros
Use concrete manipulatives, such as the base 10-block set. Procedural fluence must follow conceptual understanding.
Why do students misinterpret a division problem like 20 ÷ 4 as either 20 – 4 or 4 × something.
Confusion between Division and Subtraction or Multiplication symbols.
How do you distinguish a mistake from a conceptual error?
Mistakes are random and not systematic, while a conceptual error is repetitive for the same type of problems.
What challenges do students have with a problem 403 + 214?
Believing a zero “disappears” or has no value in addition contexts.
How do you correct the misconception that 1/3 > 1/2
The best way is to use concrete manipulatives, such as number strips.
What is the reason for a student to write
5.2 – 3.45=3.07?
Misalignment of place values because of a weak understanding of place value and decimal representations.
Why do students struggle with multi-digit division, especially aligning numbers and handling remainders.
Weak place value understanding and limited practice decomposing numbers.
Why is the knowledge of place value fundamental to the success of students in working on operations?
It enables them to understand the value of digits in numbers, which is essential for accurately performing addition, subtraction, multiplication, and division.
Give an example of a weak number sense for students in grade 6
Limited understanding of the relationship between numbers (e.g., 49 + 25 is the same as 50 + 24).
How do you correct 1/4 + 1/2 = 2/6
Teach equivalence and use manipulatives such as fraction strips
What is the reason for reliance on a standard algorithm rather than using flexible strategies (e.g., counting up, number lines).
Example: Not recognizing that 91 – 89 can be solved mentally using number sense.
Lack of Strategic Thinking
Overemphasis on formal methods over mental math and reasoning.
What learning gap does the scenario below tell you as a teacher?
Students are unsure what to do with remainders or interpret them incorrectly in word problems.
Lack of contextual understanding (e.g., when to round up or ignore a remainder in real-life scenarios).