Template For Project Chapter 4 With Reteach

Name: Miss Almendarez

Grade Level: 4th Grade

Title of Lesson: Divisibility

Texas Essential Knowledge and Skills/Standards: Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(A) apply mathematics to problems arising in everyday life, society, and the workplace;

(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

(E) create and use representations to organize, record, and communicate mathematical ideas;

(F) analyze mathematical relationships to connect and communicate mathematical ideas; and

(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Objective/Purpose: To be able to precisely explain what divisibility means. To be able to determine if the numbers are divisible by other numbers.

Introduce Lesson: First, ask the class for the definition of divisibility. If the students do not know the definition then proceed to tell them that divisibility is an abbreviated or shortened exam to see if a number is divisible by another number, without having to do the actual division problem. Next, talk briefly about the historical background of divisibility, who came up with this concept, and why. For instance, the first people who came up with divisibility rules were Islamic mathematicians. In the earlier years of 9801073 AD, Ibn Sina, was the first person to develop an idea of “casting out 9”to determine if a number was divisible by another digit. Finally, show and explain the students the provided examples given. Example: Start with some examples of the divisibility rules to inform the students on what is expected for the lesson. Divisible by 2 if: the last digit is an even number 

Look at the last digit is it 0,2,4,6, or 8? If it is then the number is divisible by 2.

Number

Divisible Why

286

yes

6 is an even number

78

yes

8 is an even number

23

no

not an even number

Divisible by 3: if it is a multiple of 3. 

Add the digits and then determine the multiples of 3 and see if it is divisible by 3.

Number

Divisible

Why

207

yes

2+0+7=9, 9 is a multiple of 3.

480

yes

4+8+0=12, 12 is a multiple of 3.

515

no

5+1+5=11,11 is not a multiple of 3.

Divisible by 4: If the last two digits are a multiple of 4 (or if the last two digits are 00). 

Look at the last two digits and determine the number that is a multiple of 4 and test to see if it is divisible by 4.

Number

Divisible Why

348

yes

48 is multiple of 4

722

no

22 is not a multiple of 4

1,200

yes

the last two digits are 00 and 200 is a multiple of 4.

Lesson: First, after you finish the intro lesson about divisibility, go over the rules of divisibility for numbers two, three, and four. Either write out each example given on the white board or use the overhead projector for the examples that I have provided for you. Ask the students if they have questions; allow at least a minute for a response. Next, after the lecture, ask them politely to get into groups of 4 and instruct them to get out a pencil. Next, I have printed out a worksheet for them to complete as a group. Also, tell them to answer only the questions which are divisible by two, three, and four. The students will be given five minutes to complete the worksheet fully. Please stress to them, if needed, the rules of divisibility or hint to them and guide the student struggling, but do not give them the answer. The students need to be able to think and work together as a group. When the first group is finished, have all participants stand up in front of the classroom to check and make sure all of the answers are correct. Then the winning group will be able to pick a prize from my treasure chest. Worksheet:

Re-Teach: When all the students are working in their groups, you can either sit with the students and guide them throughout the activity with the group and give hints and explain to them. Also, you can pull any struggling student and go to my back table to review notes and examples and let the student try the examples with your guidance so that the student gets a one on one. This will allow the student to ask questions in order to help that student understand the concept of divisibility.

References 

https://www.google.com/search? rlz=1C1CHFX_enUS701US701&tbm=isch&q=divisibility+rules+worksheet&chi ps=q:divisibility+rules+worksheet,g_1:4th+grade



https://www.emis.de/journals/BMMSS/pdf/v22n1/v22n1p4.pdf



http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111a.html#111.6