AGE: From 6 years (after the child has been introduced to this activity Part 1)
OBJECTIVE(S):
1.To provide your child a sensorial experience of addition by making 10s with
different combinations of numbers from the colored bead stair: a.Understand that a 10 can be made out of 2 or more bead bars. b.See that the colored bead bars making a ten is the same length
as the 10 bar. c.See the different patterns made by the bead bars.
2.To prepare your child for the Montessori Positive Snake Game. 3. To train the creativity of your child in coming up with different combinations of 10
MATERIALS:
1.1 set of Decanomial Bead Bars - a box with 10 compartments containing 55 of each colored bead
bars from 1-10.
2.1 mat.
PRESENTATION:
1. Place a golden 10-bar vertically on the mat and count it.
2. Make it into a game and take turns to make different combinations of 10. For example, let your child choose a colored bead bar from the box. If he picks a 7-bar, place it next to the 10-bar and count 7.
3. Ask, "What other color bead bar(s) can we combine to make 10?" Let him choose the remaining colored bead stair(s) to make 10, i.e. he may choose 3-bar.
4. Place the color bead bars side-by-side against the 10-bar and count them to verify the answer.
5. Let him try out all the different combinations of 10 that he could come up with.
6. Ask, "Are you sure you have gotten ALL combinations possible? Shall we try a systematic way of combining them to ensure that?"
7. Show him the systematic way of getting all the combinations of 10s by:
7a. starting with combining blue 9-bar and 1-bar. It gives 1 combination.
7b. Show him the different combinations of 10s with brown 8-bars - it gives 2 combinations.
7c. Show him the different combinations of 10s with white 7-bars - it gives 3 combinations.
7d. Show him the different combinations of 10s with purple 6-bars - it gives 5 combinations.
7e. Show him the different combinations of 10s with light blue 5-bars - it gives 7 combinations.
7f. Show him the different combinations of 10s with yellow 4-bars - it gives 9 combinations.
7g. Show him the different combinations of 10s with pink 3-bars - it gives 8 combinations.
7h. Show him the different combinations of 10s with green 2-bars - it gives 5 combinations.
7i. Show him the different combinations of 10s with red 1-bars - it gives 1 combination.
8. Show your child that you have obtained all complete 40 combinations. Notice that we ran out of red 1-bars, so we use unit golden beads instead.
REFERENCES:
Shu-Chen Jenny Yen’s
On-line Montessori Albums http://faculty.fullerton.edu/syen/mts/math/_link.htm ADDITIONAL INFORMATION:
Our Little FECS (6Y1M28D) has lately been very interested in making these different combinations of 10. I thought of a systematic way of showing him how to get all the combinations. Before I showed him combinations of each number, he first guessed how many combinations it would get. He guessed 6-7 combinations for 5-bars, and got it correct. He guessed 11 combinations for 4 bars, which was incorrect. It was fun making guesses and verifying the answer by placing all the beads. This activity can be played without seeing Part 1 lesson plan, but you can find Part 1 lesson plan here.
1.Place a golden 10-bar vertically on the mat and count it.
2.Make it into a game and take turns to make different combinations of 10. For example, let your child choose a colored bead bar from the box. If he picks a 7-bar, place it next to the 10-bar and count 7.
3.Ask, "What other color bead bar(s) can we combine to make 10?" Let him choose the remaining colored bead stair(s) to make 10, i.e. he may choose 3-bar.
4.Place the color bead bars side-by-side against the 10-bar and count them to verify the answer.
5. Let him try out all the different combinations of 10 that he could come up with.
6. Ask, "Are you sure you have gotten ALL combinations possible? Shall we try a systematic way of combining them to ensure that?"
6. Ask, "Are you sure you have gotten ALL combinations possible? Shall we try a systematic way of combining them to ensure that?"
7a. Show him the systematic way of getting all the combinations of 10s by starting with combining blue 9-bar and 1-bar. It gives 1 combination.
7b. Show him the different combinations of 10s with brown 8-bars - it gives 2 combinations.
7c. Show him the different combinations of 10s with white 7-bars - it gives 3 combinations.
7d. Show him the different combinations of 10s with purple 6-bars - it gives 5 combinations.
7e. Show him the different combinations of 10s with light blue 5-bars - it gives 7 combinations.
7f. Show him the different combinations of 10s with yellow 4-bars - it gives 9 combinations.
7g. Show him the different combinations of 10s with pink 3-bars - it gives 8 combinations.
7h. Show him the different combinations of 10s with green 2-bars - it gives 5 combinations.
7i. Show him the different combinations of 10s with red 1-bars - it gives 1 combination.
Here are the completed 40 possible combinations :-) Notice that we did not have sufficient red 1-bars, so we substituted with unit golden beads instead.
1 May 2015 (6Y1M26D): Making combinations of 10 with colored bead stair
Our Little FECS requested to work on making combinations of 10 with colored bead stair today. It was exactly 1 year since we first worked on this. What a difference 1 year made. He has matured a lot since. This time round, he really had a lot of fun. He is older and more independent, and he thought up many different combinations himself. It took very long, and it was way past bedtime at 9pm. He had completed 29 different combination and the rest tomorrow. So we agreed that he would continue tomorrow.
AGE: 5 to 6 years (after the child has worked with the Positive Snake Game, Linear and Skip Counting * to do this exercise. This exercise is the second verification of the above. (* Chains introduce child to concept of 3 sets of 3, etc.)
OBJECTIVE(S):
1. To help your child to understand the concept of multiplication in a visual and sensorial way:
- Multiplication (乘法) is adding the same number over and over again (乘法是一次又一次地添加相同的数量。)
- Multiplicand (被乘数[bèi chéng shù]) is the number that gets multiplied
- Multiplier (乘数 [chéng shù]) is the number that you are multiplying by.
MATERIALS:
1. 1 set of Decanomial Bead Bars - a box with 10 compartments containing 55 of each colored bead bars from 1-10.
2. 1 multiplication worksheet, pencil and eraser (later in presentation) or time table cards (optional)
3. 1 mat.
PRESENTATION I: SENSORIAL
1. Start with time table 2 (乘法表2).
2. To provide a sensorial feel of multiplication, arrange the green 2-bars horizontally from 2x1… 2x10 and say, “1 set of 2, 2 sets of 2, 3 sets of 2, 4 sets of 2… 10 sets of 2, but don’t say the answers.
(In Chinese, say "一个二，两个二，三个二，四个二… 十个二)
3. Repeat the process with another set of time table.
4. Lastly, you can place the time table card next to each set.
5. For variation: You can also arrange the green 2-bars (for timetable 2) one set at a time, adding another bar to make the next set.
12 May 2014 (5y2m7d): Adding one bar at a time
12 May 2014 (5y2m7d)
12 May 2014 (5y2m7d): Adding one bar at a time
PRESENTATION II: SENSORIAL - MAKING COMBINATIONS OF MULTIPLICATION
1. Place a golden 10-bar, add a green 2-bar, thus making 12 vertically on the mat.
2. Ask the child to make as many combinations as possible which will total 12.
3. Show the child that 6x2 is the same as 2x6 etc. and explain, “6 sets of 2 = 12", and "2 sets of 6 = 12." (In Chinese say, "六个二等于十二, 两个六等于十二"
4. The child should be able to make the following combinations – 2 sets of 6, 3 sets of 4, 4 sets of 3, 6 sets of 2 and 12 sets of 1.
PRESENTATION III: TABLE
1. Start with multiplication table 3, 4, 5, 6, 7, 8, 9. In this example, we will show 2.
2. Place a green 2-bar horizontally on the mat and say, “This is 1 set of 2 i.e. 2x1 (two times one). You have two 1 time” and count the beads “1,2”
3. For the answer, place another green 2-bar vertically under the first green 2-bar and say, “The answer is 2. 2x1=2.”
4. Place 2 green 2-bars horizontally on the mat on the right of the first 2-bar and say, “This is 2 sets of 2 i.e 2x2 (two times two). You have two 2 times” and count it “1,2,3, 4.”
5. Place a yellow 4-bar under the 2 green 2-bars and say, “The answer is 4. 2x2=4.”
6. Continue in the same manner until 2x10=20.
7. Note: There won’t be enough bead bars to do all the problems. For quantities over 10, use golden bead bars and colored bead bars.
8. When this has been completed, return to the first set of 2 and ask, "How many sets of 2 is this?" The answer will be "This is 1 set of 2", and continue to 10.
9. Next say, “2 sets of 2 equal 4.”
10. Invite the child to write the answer in the worksheet.
11. Repeat the process with another number time table.
1. Comparing the quantities of bead bars.
2. Multiplication chart.
REFERENCES:
http://www.montessorialbum.com/montessori/index.php?title=Multiplication_With_Bead_Bars http://faculty.fullerton.edu/syen/mts/math/8-3.htm http://www.infomontessori.com/mathematics/tables-of-arithmetic-multiplication-bead.htm ADDITIONAL INFORMATION: J (5y2m7d) tried the presentation I for the first time this evening. He was able to understand the concept and he said the number of twos gives... Updates 26 May 2016 (7Y2M21D) Since I returned back to full time work for the last 4 months, Montessori has taken a backseat. Today, he has no play date. My mum picked him up earlier at 3pm, so that we could do Montessori, before he went off for his music class. Thankfully, our baby was sleeping, so that we could have uninterrupted time. He chose to first write the 2 time-table by pencil. He could do it completely. Then I asked him to construct it with beads to make sure that he understood the concept. I asked him to say, 2 x 2 means 2 taken 2 times in mandarin... he wasn't so keen to say it. I also ask him to count that there are 9 bars in 2 x 9. We also did skip-counting... 2, 4, 6, 8, 10, 12, 14... etc. so that he understood the concept of time table. I randomly asked him the 2 time-table, that was a little more challenging.
The Decanomial Bead Box is available from Amazon:
26 May 2016 (7Y2M21D)
26 May 2016 (7Y2M21D): Multiplication with Bead Bars
AGE: 4.5 to 6 years (after the child has worked with addition with red
rods, has mastered the colored bead stair and plus and equal exercises)
OBJECTIVE(S):
1.To teach counting and addition of the unit place value in a
concrete manner.
2.To tech the definition of addend (加数 [jiā shù]): a number to be added to another (Addend + Addend = Sum)
MATERIALS:
1.2 sets of colored bead stair
2.3 felt pieces or colored paper
3.1 addition worksheet
4.1 pencil and eraser
PRESENTATION:
1.Lay out the colored bead stairs on the left and right of the
worksheet.
2.Have your child read the first question: “1+3=?”
3.Have your child pick the first addend red 1-bar from the left
colored bead stair, count it and place it on the mat.
4.Have your child pick the second addend pink 3-bar from the right
colored bead stairs, count it and place it on the mat, making sure that the
beads are not taken from the same colored bead stair.
5.Have your child place both bead bars in a line on the mat.
6.Have the child count the total number of beads: “1,2,3…”
7.Ask the child write or paste the result onto the equation and say:
“1+3=4”.
8.Return the colored bead stair and encourage your child to try the
different combinations from the worksheet.
9.Later: Introduce written equations as outlined in Addition with
the Table-Top Numerical Rods.
CONTROL OF ERROR:
1.The child's knowledge of numbers.
2.Verification by the teacher.
3.Addition Control Chart.
VARIATIONS:
1.Other materials may be substituted for the bead bars, such as
shells, buttons and so on.
I tried this with J on 5 May 2014 (5Y2M0D). It was too easy for him at this age. He could do it and he had also memorized the color bead number. Soon after, he was doing the calculation mentally in his head. However, whenever he made a careless mistake calculating in his head, I asked him to verify the answer by using the color bead stair. So this activity served as a control of error for his mental calculation.
