Embedded Files
Indonesian Curriculum Standard for Math Lesson
Capaian Matematika.pdfSource: SK Kemendikdasmen No. 046/H/KR/2025
Please have a look first for the Indonesia curriculum standard for math lesson. From here we're focusing on Numbers that said "Number is the field of study that discusses numerals as number symbols, the concept of number, number operations (arithmetic), and the relations between various number operations within the sub-elements of visual representation, order properties, and operations".
Big Idea Statement
So, the big idea based on students' challenges and Indonesian curriculum standard is Making lesson plan for mathematics lesson of integer problems on 4th grade for 3 weeks (2 x 35 Minutes/Week).
Concept Map
Source: https://notebooklm.google.com/
Learning Outcome
Conceptual Focus
Evidence of Transfer
Common Misconceptions
Understanding that integers consist of negative numbers, zero, and positive numbers, representing a pair of opposites relative to the center point of 0.
Basic Integer Concept
Negative Transfer: Students treat negative numbers like ordinary whole numbers, failing to define 0 as neutral. They may think −0 is different from 0.
Understanding that the value of an integer is determined by its directional position on the Number Line; the further to the left, the smaller the value.
Ordering Integers
The student can correctly order the numbers 3,−5,0,−2,1 and explain why −5 is less than −2 (because it is further to the left of 0).
Magnitude Error: Students focus on the absolute value (distance from 0) and believe −5>−2 because 5 is numerically larger than 2.
Understanding operations as directional movement on the Number Line or as a process of neutralization (cancellation) between positive and negative quantities.
Addition and Subtraction Integer
The student can solve −3+7 using a manipulative model (colored chips/counters) or movement on the number line, explaining that 3 negatives are cancelled by 3 positives, leaving 4 positives.
Sign/Operation Confusion: Errors in confusing the number's sign with the operation's sign. Example: The student calculates 5−(−3) as 5−3=2 (ignoring the second negative sign) or solves −5+3 as −8 (assuming addition always increases the magnitude).
How This Unit Builds from Surface to Transfer?
Surface Learning: Building Fluency and Facts
Surface Learning: Building Fluency and Facts
Surface learning focuses on the acquisition of basic knowledge and skills—the facts and procedures students must recognize and recall. In the integer unit, this phase addresses the Basic Integer Concept and initial Ordering. Students must first memorize the names, symbols, and rules.
Focus: Students identify and read positive and negative numbers. They learn the vocabulary like "opposite" (of a number) and "absolute value" (distance from zero). They practice simple one-step procedures, such as correctly plotting a single integer on a number line or converting a simple contextual phrase ("4 steps back") into the symbol −4. They achieve fluency in basic representation.
Deep Learning: Integrating Concepts and Justification
Deep Learning: Integrating Concepts and Justification
Deep learning involves connecting, justifying, and structuring knowledge around the Big Idea—that integers are a system of opposites centered at zero. This phase tackles the complexities of Ordering and the introduction of Addition/Subtraction through modeling.
Focus: Students shift from plotting numbers to comparing them. They move from simple memory to conceptual justification, explaining why −5 is less than −2 using the number line (position) or the debt model (less money is worse). They use manipulatives (like two-color counters) to model −3+5 and verbally justify the answer 2 by explaining the process of neutralization (3 positive counters cancelling 3 negative ones). This builds a flexible understanding, moving beyond rote rules.
Transfer Learning: Applying Knowledge to New Contexts
Transfer Learning: Applying Knowledge to New Contexts
Transfer learning is the highest level of understanding, where students can flexibly use their conceptual knowledge to solve novel, multi-step problems that are outside the initial instructional context. This phase culminates in mastery of Addition/Subtraction and tackling Word Problems.
Focus: Students are given complex, multi-step word problems (e.g., "An airplane is 5,000 feet above sea level and a submarine is 500 feet below. If the plane drops 3,000 feet, what is the new vertical distance between them?"). They must select the appropriate model (number line or equation), convert context to symbols (5000,−500), calculate the solution, and critically evaluate their result. This demonstrates true mastery, as they can apply the Big Idea of direction, distance, and opposites in completely new situations.
This unit achieves deep, transferable learning by first establishing surface fluency in identifying integer symbols and vocabulary, then progressing to deep conceptual mastery through the modeling of neutralization and directional movement, which finally enables students to transfer this understanding to solve and justify complex, novel real-world problems.
Page updated
Report abuse