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Grade 1 Academic Situations
Numbers and Operations
Key Points:
Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.
Common Struggles:
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Carrying Addition within 20: Students know the basic method for carrying addition within 20 but lack proficiency. For example, incorrectly calculating 8+5 as 12. Errors are more common when adding 6, 7, or 8 (accuracy with adding 9 is slightly better, with 8 being the most problematic). For example, mistakes in addition calculations.
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When writing answers, reversing the digits. For example, writing the answer 12 as 21.
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Number Recognition: Knowledge of number recognition is not firmly grasped, leading to confusion about the magnitude relationship between numbers, as well as the order and position of digits. For example, numbers like 34 and 43, 25 and 52, etc., are easily confused.
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In basic addition and subtraction, when performing operations with carrying or borrowing, students easily forget the ""1"" that needs to be carried or borrowed. For example, incorrectly calculating 35+7 as 32.
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Careless in problem-solving, not focusing on the key points. For example, which number is closest to 70? (68, 80, 71)
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Prone to inertia in thinking during problem-solving, influenced by previous problem-solving habits, and only using one type of thinking pattern to solve problems. For example: There are 17 apples in total, 9 are left, how many did the little squirrel take
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Prone to missing or adding words during problem-solving, leading to misunderstandings of the problem. For example: 40 jump ropes are distributed among the classmates, each person gets one and there are still 8 short, how many people are in the class?
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Weak memory, lack of concentration, and insufficient proficiency, leading to carelessness in solving problems. For example: Copying numbers incorrectly or mistaking addition and subtraction signs.
Solution:
Impact on Knowledge: Mastery of addition and subtraction within 20, and addition within 100, is fundamental for second graders to advance their understanding and calculation of larger numbers. The first grade is a crucial phase for laying a strong foundation in these arithmetic operations. A deep understanding of addition and subtraction will also significantly affect learning multiplication and division in the third grade.
Impact on Scores: Although there are no written exams in the first and second grades, written exams begin in the third grade. This leads many third-grade teachers to jokingly refer to a student's first exam as ""opening a blind box."" At this point, proficiency in calculation becomes especially important. In the third-grade exams, calculations have a high weight, and computational skills are also needed for solving application problems. Therefore, points are often lost due to lack of fluency in calculations, which is regrettable.
Impact on Interest: Although learning calculations can be somewhat dry, practice makes it easier to achieve a high degree of proficiency. As computational skills improve, confidence in learning gradually increases, which in turn generates an interest in learning.
Geometry
Key Points:
Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.
Common Struggles:
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Reason with shapes and their attributes.
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Distinguish between defining attributes (e.g., triangles are closed and
three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. -
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
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Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
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Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares."
Solution:
Starting with actual objects from everyday life, students can concretely understand solid shapes and begin to classify them. This lays a solid foundation for later observing solid figures and understanding their characteristics.
Measurement and Data
Key Points:
Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.
Time: Tell and write time in hours and half-hours using analog and digital clocks.
Data: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
Common Struggles:
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This is the students first time learning about time, due to the prevalent use of digital clocks in daily life, such as those on mobile phones, many students are not familiar with traditional clocks and are unable to distinguish between the hour and minute hands, nor can they accurately read or write time.
Solution:
Understanding clocks is the initial attempt for students to establish a concept of time. It lays a solid foundation for subsequent learning, such as understanding half-past times, exact minutes past the hour, and calculations related to time. For example, when learning about 3:20 on a clock in the second grade, students should already know from the first grade about the hour and minute hands, as well as the fact that each big mark on the clock face represents 1 hour for the hour hand and 5 minutes for the minute hand.
Consequences
Calculations:
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Unclear understanding of mathematical principles, slow calculation speed, entirely relying on counting with fingers.
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Non-standard handwriting and format lead to calculation errors.
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Mistakes in copying numbers or misreading them, for example, writing 3 looking like 5.
Geometry:
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Lack of orderly thinking: counting objects in an unordered manner, leading to repetitive counting or omission.
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Insufficient spatial sense and geometric intuition: children lack intuitive feelings for shapes and have not undergone related training and development.
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Word Problems:
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Inability to analyze problems, not valuing reading the problem, and reliance on teachers or parents to read the questions.
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Misunderstanding information in pictures, often confusing addition and subtraction.
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Insecure calculation skills, leading to correct equations but wrong results.
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Fear of difficult problems, starting to fiddle with fingers at the sight of application questions, unwilling to try.