The chosen standard
According to the norms, adopted by State Board of Education of Public Schools of North Caroline, third-grade students should be able to “represent and solve problems involving multiplication and division” (2011, p. 15). They need to see how equations can be applied. On the whole, these skills are critical for the academic performance of a child and his/her ability to understand mathematics and natural sciences. Additionally, the failure to understand such notions as a multiple or a quotient can undermine subsequent academic performance of a child. This is why this requirement should not be overlooked by teachers who work with third-grade students. Moreover, on the basis of this standard, one can develop several distinct goals that a teacher should attain in the course of a lesson.
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It is possible to identify several goals that should be attained by the educator.
- A student should be able to solve equations involving division and multiplication.
- A learner can apply these mathematical operations to real-life situations.
- A student can interpret the notions of a product and a quotient.
By achieving these goals, a teacher can give students deeper insights into the nature of various mathematical operations. More importantly, it is critical to show that these mathematical operations can be applied in various ways.
Specific learning objectives
Each of these instructions goals can give rise to various learning objectives. These objectives are related to the specific and measurable behaviors of students.
First instructional goal
- A learner can identify the unknown number in such equations as 8×X=100 or 8×X =48.5. It should be noted that the unknown variable can occupy different places in such equations. One should remember that in many cases, learners find it difficult to cope with mathematical problems, because they are not accustomed to solving various types of equations.
- Proficiency level: Students are able to solve mathematical equations involving multiplication of natural numbers and integers. They correctly identify the unknown number in such equations as 8×X=100 or 8×X =48.5. They can correctly resolve at least 8 of the ten tasks that will be assigned to them.
- A student can determine the number which solves such equations as 56 ÷ x=8, X÷ 4=2,5. It should be mentioned that students operate both the integers and the decimal fractions. Very often, learners struggle with the divisions of decimal fractions.
- Proficiency level: Learners can determine the unknown number in the equations like 81 ÷ x=9 or 5÷ x=2,5. They can correctly resolve at least 8 out the ten equations given to them.
- A learner is supposed to do tasks which combine multiplication with addition. For example, one can speak about 4(x+20)=100. The students should keep in mind that multiplication is governed by the distributive law which is critical for various mathematical operations.
- Proficiency level: A student is able to solve the equations combining multiplication and addition. For example, one can speak about the following equations, 5(x+10)= 75; 2(x+10)=22.
Second instructional goal
- A learner can represent word problems in the form of equations
- Proficiency level: Students can represent at least 90 percent of word problems in the form of equations.
- A student can solve word problems involving multiplication and division
- Proficiency level: Learners can solve at least 80 percent of the word problems which are assigned to them.
- Students should compose word problems to incorporate mathematical operations.
- Proficiency level: Students can compose at least five word problems on their own.
Third instructional goal
- Students can interpret visual images describing the process of multiplication or addition.
- Proficiency level: Students can determine which of the mathematical operations, namely addition or subtraction, is depicted in the picture.
- Learners can correctly interpret the notions of a quotient.
- Proficiency level: Students can correctly identify which of the presented images depict the division process.
- Finally, a student should learn to see the connection between multiplication and addition.
- Proficiency level: They should be able to represent equations like 7+7+7= 21 with the help of the multiplication process, namely 7× 3=21.
Justification of the objectives
They need to see that this unknown can be placed in various parts of the equation. This skill will be important for solving more complex mathematical tasks. Moreover, they need to understand how multiplication and division can be applied to integers and decimal fractions. By achieving these objectives, learners can better cope with the tasks related to natural sciences.
The second instructional goal is related to the ability of students to solve word problems. They need to show that in some situations, a verbal question can be transformed into an equation. Moreover, the learners should see that the knowledge of these mathematical operations is important for everyday life of a person. In this way, a teacher can better engage learners into the learning process. They need to see that many tasks can be formalized with the help of an equation. Moreover, the attainment of these objectives is vital for the proficiency in other subjects such as chemistry or physics.
Finally, the learners should demonstrate understanding of the essence of mathematical operations. For example, they need to remember that division can be compared to partitioning. Furthermore, they should see that multiplication involves equal groups or sets of objects. This is one of the reasons why students should analyze visual objects and drawings. Moreover, they need to see the connections between multiplication and addition because this understanding will help them cope with more complex mathematical problems.
Public Schools of North Carolina. (2011). North Carolina Extended Common Core State Standards Mathematics K-5.( NC Extended CCSS Final). Web.