SeSEM Mathematics
These problems attempt to bring many elements such as biology, diversity awareness, faith education, drama, etc together with mathematics and to present them in the integrated, undivided way they're found in life.
Math that is more elemental can be done outdoors without the use of pen and paper to fortify the memory, mind, working memory and concentration, for ex, while picking fruits or climbing trees. Moreover, breathing fresh air and oxygen will be a means of helping children's brains work more clearly and exposure to sunlight will be a means of their bodies acquiring much needed Vitamin D.
Q. ETIENNE LEFT HIS POETRY AT HOME
Etienne loved walking to the children's house with his dad. On the way, they wave "salaam!", "peace!" at the cotton-like clouds in the sky, they wave salaam at the pretty flowers and they say salaam to the rabbit hopping. It takes them 10 minutes to walk from home to the children's house. This morning just as Etienne arrived at the children's house, he realized he left the poem he had written last night at home. He really wanted to recite his poem to his friends and educators. He wanted his friends to appreciate the talent God gave him. So he asked his dad: "Will you take me back home so I can bring my poetry to the children's house." His dad loved that Etienne enjoys poetry and replied, "of course." So they went back home to pick up the poem. They said salaam to the neighbor's cat on the way and Etienne found a pretty spiky pine cone to take home to remind him of God's Divine Beauty. Then they walked all the way back to the children's house again. They said salaam to the squirrels and they said salaam to the birds. How long did Etienne walk in total this morning?
Picture Ideas:
Frame #1: J
A. ***10+10+10=10*3=30*** This is a good incident to discuss the relationship between addition and multiplication. This too can be acted out with little dolls or toys walking "lalalalalaalaa, salaam, lalalalalaalaa, salaam!" :)
If one of the children don't mention it, bring this to their attention: The question doesn't specify how many minutes it took them to walk from the children's house to home and then back to the children's house. In the answer we have assumed that they walked at the same speed. Had they walked slower or faster, accordingly they would have taken longer or shorter to reach home/the children's house. This is just the opportunity to discuss the relationship between time and speed, when the distance is the same. At the same time, this is a practice of critical reading and analysis. A textbook is not a book of 100% incontestable truths, there may be mistakes and shortcomings, everyone needs to search the truth for their ownselves.
Q. JEHAN MEASURING HER EYES
Jehan loves both science and art. Today she got very excited because she found a scientific fact in her art book. She learned that the distance between her eyes were created exactly the same as the length of each eye. Jehan marveled at the mathematical miracles of God on her very own face. Being a science girl, she decided she must test this for herself, so she can confirm it. She went to find a measuring tape. Then she started thinking: what is the quickest way I can measure my eyes and know whether it's true? Can you help Jehan?
Picture Ideas:
Frame #1: Jehan in an art room with arched stained glass windows looking onto a garden with a fountain, painting planets and lab desks on easels, building solar system maquettes and such nerdy artsy things.
Picture #2: Jehan surprised looking onto a graphic drawing of a human face in an art book, where the face is divided into symmetrical portions
Picture#3: this should be a simple schema focusing on the eyes of the face and indicating said distances.
Picture #4: Jehan looking into a mirror with light shining out of her face, because she has come to the realization that “my face is a Divine Mirror!” (in a “thought bubble” coming out of her head)
Picture#5: Jehan fetching the measuring tape out of a drawer
Picture#6: Jehan with a "?" above the head, holding the measuring tape around her eyes awkwardly in front of a mirror, as if to decide how to exactly hold the tape (ie what to measure) (thought bubble: O Divine Guide, guide me to the correct answer)
A. ***Open ended question. Give the students tapes and let them discuss in small groups their ideas. Some ideas to be offered if no student comes up with them:
- Measure the length of one eye=x. Then measure the entire length from the beginning of one eye to the end of the other eye=y. See that in fact y=3x
- Measure the length of each eye (perhaps you want to confirm that the eyes are of the same length to begin with), and the distance in between and confirm they're all the same.
- Measure the length of one eye=x. Then measure the entire length from the beginning of one eye to only the beginning of the other eye=y. Notice there are two ways to measure y. See that in fact y=2x
- Measure the length of one eye and the distance in between and confirm they're the same.
- Measure the distance in between eyes=x. Then measure the entire length from the beginning of one eye to the end of the other eye=y. See that in fact y=3x
- Measure the distance in between eyes=x. Then measure the entire length from the beginning of one eye to only the beginning of the other eye=y. See that in fact y=2x.
Also encourage them to go ahead with performing the multiplication by continuing to the 2nd part of the question:
Q. Jehan measured the distance between her eyes to be 25 mm. She wanted to be sure she measured herself correctly. She picked up a science book to verify her measurement. She found out that humans older than 13 have an average eye length of 24mm. Jehan also found out there can be 1 or 2 mm variation in eye length between humans. Jehan was 14 years old. Do you think her measurement could be correct? What was the distance from the beginning of her left eye to the end of her right eye?
Picture Ideas:
Frame #1: Jehan measuring the distance between her eyes, close shot on Jehan’s face facing the mirror.
Frame #2: Jehan reading a biology book with pictures of eyes. (thought bubble: O Divine Source of Knowledge, give me knowledge)
Frame #3: Graphic showing the length of eyes and variation
Frame #4: Show Jehan measuring from the beginning of her left eye to the end of her right eye, again with close shot on Jehan’s face facing the mirror.
A. ***Yes, her measurement could be correct. Discuss that if mean&variation: 24+ or - 1 or 2, then range is 22 to 26 and 25 falls in this range.*** To show this draw an average eye and superpose slightly smaller and larger eyes.
***25*3=75mm*** They can try both mental and paper calculation. I would certainly discourage calculators at this low level of math. Loud discussion of mental calculation can be encouraged so they can freely share their personal mental multiplication techniques. Stress importance of providing units in the answer. 75 what? 75 cows? 75 yards? etc.
Now you can also discuss more subtle concepts with an audience ready to grasp: Are they sure their measurement is, say 23? Is it perhaps, 22.9 or 23.1 or 23.0001? If they don't know decimals yet, you can point out that the tape has many more divisions between integers. You can tell them there are numbers for just a tad bit bigger than 23 but not as big as 24. Bring to their attention that infinity is not only in greatness but also in minuteness. Marvel at how God can fit infinitely many small differences (i.e. different real #s) in a tiny space on the tape. This will give them a very basic foundation for the understanding of the fields of calculus, analysis (real&numerical), statistics, all measurement problems in natural sciences, as well as the concepts of "continuous and discrete variables". Compare and contrast that you can have 3 or 4 stones (discrete variable) but not something in between (like 3.5 stones!) but the measuring tape counts differently (continuous variable). You could mention these terms but without emphasizing them, nor expecting them to know it yet. Just being familiar should be plenty for now.
Math that is more elemental can be done outdoors without the use of pen and paper to fortify the memory, mind, working memory and concentration, for ex, while picking fruits or climbing trees. Moreover, breathing fresh air and oxygen will be a means of helping children's brains work more clearly and exposure to sunlight will be a means of their bodies acquiring much needed Vitamin D.
Q. ETIENNE LEFT HIS POETRY AT HOME
Etienne loved walking to the children's house with his dad. On the way, they wave "salaam!", "peace!" at the cotton-like clouds in the sky, they wave salaam at the pretty flowers and they say salaam to the rabbit hopping. It takes them 10 minutes to walk from home to the children's house. This morning just as Etienne arrived at the children's house, he realized he left the poem he had written last night at home. He really wanted to recite his poem to his friends and educators. He wanted his friends to appreciate the talent God gave him. So he asked his dad: "Will you take me back home so I can bring my poetry to the children's house." His dad loved that Etienne enjoys poetry and replied, "of course." So they went back home to pick up the poem. They said salaam to the neighbor's cat on the way and Etienne found a pretty spiky pine cone to take home to remind him of God's Divine Beauty. Then they walked all the way back to the children's house again. They said salaam to the squirrels and they said salaam to the birds. How long did Etienne walk in total this morning?
Picture Ideas:
Frame #1: J
A. ***10+10+10=10*3=30*** This is a good incident to discuss the relationship between addition and multiplication. This too can be acted out with little dolls or toys walking "lalalalalaalaa, salaam, lalalalalaalaa, salaam!" :)
If one of the children don't mention it, bring this to their attention: The question doesn't specify how many minutes it took them to walk from the children's house to home and then back to the children's house. In the answer we have assumed that they walked at the same speed. Had they walked slower or faster, accordingly they would have taken longer or shorter to reach home/the children's house. This is just the opportunity to discuss the relationship between time and speed, when the distance is the same. At the same time, this is a practice of critical reading and analysis. A textbook is not a book of 100% incontestable truths, there may be mistakes and shortcomings, everyone needs to search the truth for their ownselves.
Q. JEHAN MEASURING HER EYES
Jehan loves both science and art. Today she got very excited because she found a scientific fact in her art book. She learned that the distance between her eyes were created exactly the same as the length of each eye. Jehan marveled at the mathematical miracles of God on her very own face. Being a science girl, she decided she must test this for herself, so she can confirm it. She went to find a measuring tape. Then she started thinking: what is the quickest way I can measure my eyes and know whether it's true? Can you help Jehan?
Picture Ideas:
Frame #1: Jehan in an art room with arched stained glass windows looking onto a garden with a fountain, painting planets and lab desks on easels, building solar system maquettes and such nerdy artsy things.
Picture #2: Jehan surprised looking onto a graphic drawing of a human face in an art book, where the face is divided into symmetrical portions
Picture#3: this should be a simple schema focusing on the eyes of the face and indicating said distances.
Picture #4: Jehan looking into a mirror with light shining out of her face, because she has come to the realization that “my face is a Divine Mirror!” (in a “thought bubble” coming out of her head)
Picture#5: Jehan fetching the measuring tape out of a drawer
Picture#6: Jehan with a "?" above the head, holding the measuring tape around her eyes awkwardly in front of a mirror, as if to decide how to exactly hold the tape (ie what to measure) (thought bubble: O Divine Guide, guide me to the correct answer)
A. ***Open ended question. Give the students tapes and let them discuss in small groups their ideas. Some ideas to be offered if no student comes up with them:
- Measure the length of one eye=x. Then measure the entire length from the beginning of one eye to the end of the other eye=y. See that in fact y=3x
- Measure the length of each eye (perhaps you want to confirm that the eyes are of the same length to begin with), and the distance in between and confirm they're all the same.
- Measure the length of one eye=x. Then measure the entire length from the beginning of one eye to only the beginning of the other eye=y. Notice there are two ways to measure y. See that in fact y=2x
- Measure the length of one eye and the distance in between and confirm they're the same.
- Measure the distance in between eyes=x. Then measure the entire length from the beginning of one eye to the end of the other eye=y. See that in fact y=3x
- Measure the distance in between eyes=x. Then measure the entire length from the beginning of one eye to only the beginning of the other eye=y. See that in fact y=2x.
Also encourage them to go ahead with performing the multiplication by continuing to the 2nd part of the question:
Q. Jehan measured the distance between her eyes to be 25 mm. She wanted to be sure she measured herself correctly. She picked up a science book to verify her measurement. She found out that humans older than 13 have an average eye length of 24mm. Jehan also found out there can be 1 or 2 mm variation in eye length between humans. Jehan was 14 years old. Do you think her measurement could be correct? What was the distance from the beginning of her left eye to the end of her right eye?
Picture Ideas:
Frame #1: Jehan measuring the distance between her eyes, close shot on Jehan’s face facing the mirror.
Frame #2: Jehan reading a biology book with pictures of eyes. (thought bubble: O Divine Source of Knowledge, give me knowledge)
Frame #3: Graphic showing the length of eyes and variation
Frame #4: Show Jehan measuring from the beginning of her left eye to the end of her right eye, again with close shot on Jehan’s face facing the mirror.
A. ***Yes, her measurement could be correct. Discuss that if mean&variation: 24+ or - 1 or 2, then range is 22 to 26 and 25 falls in this range.*** To show this draw an average eye and superpose slightly smaller and larger eyes.
***25*3=75mm*** They can try both mental and paper calculation. I would certainly discourage calculators at this low level of math. Loud discussion of mental calculation can be encouraged so they can freely share their personal mental multiplication techniques. Stress importance of providing units in the answer. 75 what? 75 cows? 75 yards? etc.
Now you can also discuss more subtle concepts with an audience ready to grasp: Are they sure their measurement is, say 23? Is it perhaps, 22.9 or 23.1 or 23.0001? If they don't know decimals yet, you can point out that the tape has many more divisions between integers. You can tell them there are numbers for just a tad bit bigger than 23 but not as big as 24. Bring to their attention that infinity is not only in greatness but also in minuteness. Marvel at how God can fit infinitely many small differences (i.e. different real #s) in a tiny space on the tape. This will give them a very basic foundation for the understanding of the fields of calculus, analysis (real&numerical), statistics, all measurement problems in natural sciences, as well as the concepts of "continuous and discrete variables". Compare and contrast that you can have 3 or 4 stones (discrete variable) but not something in between (like 3.5 stones!) but the measuring tape counts differently (continuous variable). You could mention these terms but without emphasizing them, nor expecting them to know it yet. Just being familiar should be plenty for now.