The main contents of sixth-grade students' study are the operation of fractions, the mixed calculation of averages and fractions, and the addition and subtraction of decimals.
Let's look at an example first:
In the example, students are required to understand the sentence "denominator is constant, numerator is multiplied by denominator".
But in actual teaching, it is difficult for students to fully understand its meaning.
Let's look at an example first: draw two triangles on the plan and find their areas.
This problem is the operation of student scores. As can be seen from the topic, students only understand the phrase "numerator multiplied by denominator", but can't fully grasp fractional multiplication and Divison.
However, through the analysis of examples, it is found that the denominator of the topic is 0, which shows that the significance of the topic is to let students understand the multiplication and division of scores.
However, many children only understand the phrase "numerator multiplied by denominator" when solving problems, but don't understand "denominator unchanged", so they can only find a number (or array) solution when doing problems.
First, the operation of fractions
The key to this problem is to understand "numerator multiplied by denominator", that is, "denominator multiplied by fractional numerator, denominator unchanged". Many children do not fully understand this sentence.
The focus of teaching is to understand and master the significance of fractional operation.
[Teaching Difficulties] 1. Let the students understand the meaning of two fractions: 1. "1" means 1/2 or 1/3.
2. The numerator and denominator of the fraction cannot be directly calculated, and the fraction should be used instead.
Second, the average.
The concept of average is the key content of first-year students' learning, which mainly includes the concepts of average, standard deviation and variance.
According to the deduction of the concept and nature of the average, we can get the calculation formula of the average:
Where t represents the observed value (which can also be understood as the unit after the number, which determines that the average value refers to the average value of the number of data in a given interval); S stands for average interval;
[The standard deviation represents the difference between two values (usually absolute).
According to the above formula, the standard deviation is the distance between two data (unit: meter), so we call each decimal place "average".
Third, the fractional four-digit mixed calculation
After students have mastered the arithmetic of fractions, they can carry out the mixed calculation of four fractions.
In the study, we will find that:
[Teacher's comment] Through this lesson, let the children know that scores can be divisible and multiplied.
Children have mastered the meaning of dividing an integer by a fraction through previous learning, and they can also know that an integer contains a fraction, but when the divisor is more than two decimal places, division and multiplication still need to be simplified first.
[Teacher's comment] In this lesson, children are prone to make mistakes, such as using the numbers in braces as brackets.
Fourth, decimal addition or subtraction.
Let's take a look at the basics of decimal addition and subtraction.
[Primary school mathematics knowledge system]: The four parts are number theory, equation, inequality and average, among which number theory and equation should be studied in the first two semesters.
[Mathematical thinking methods in primary schools (2)]: The calculation methods of addition and subtraction of rational numbers and addition and subtraction of fractions must be mastered.
[Mathematical concept and its nature]: There are three cases of two-digit subtraction, namely, adding a pair, subtracting a pair and multiplying by one.
[Common application]: When calculating, you should be able to use corresponding methods according to known conditions and needs.