Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
Did his teacher not have the reading level from the previous year? I put kids in the level that they left off of and then work to get everyone assessed at a new level, go back a level or stay on the level. It does take time. I've been doing reading assessments since the second week of school and I'm only half the way through my students. You have to get them done when you can and when the other kids can work independently, it's not always easy with a room of 26+ students. Just email his teacher and say "my son left the previous grade at level ____, is it possible for him to take home those leveled books now?"
Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
I am so screwed when DD starts getting math homework.
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
1. Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
2. Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize — to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
3. Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
4. Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
5. Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
6. Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
7. Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + × + 1), and (x – 1)(x3 + x2 + × + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.
The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.
In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.
Post by juliahenry on Sept 30, 2013 19:41:35 GMT -5
Ok, I'm the OP here and I really was not expecting this to go to 3 pages.
I don't care about the merits of writing out steps vs doing it in your head. I can see the benefits of dividing work into stages, just as I can see the advantage of being able to work quickly in your head for basic operations.
What I do care about is
1) the work, both reading and math, is ridiculously easy. It's below grade level and it really shouldn't be, for my kid or any other kid in the class.
And 2) if you want half a page on a particular problem, and you want it done a certain way, then you need to either 1) make sure that the kid knows what's expected or 2) make sure there are instructions. My kid is bright, but he's 7. He can do the math, but he can't tell me what to do with his homework. I don't think that's a little kid's failing - I think it's a poor teaching method.
I do think the school is somewhat at fault (not the teacher, because it's a grade-wide problem with kids in other classes too), and we put a lot of time and energy into supplementing his education. I just wish they would assign meaningful, appropriate, engaging work. Homework isn't fun for any of us. But it could be, if only...
Ok, I'm the OP here and I really was not expecting this to go to 3 pages.
I don't care about the merits of writing out steps vs doing it in your head. I can see the benefits of dividing work into stages, just as I can see the advantage of being able to work quickly in your head for basic operations.
What I do care about is
1) the work, both reading and math, is ridiculously easy. It's below grade level and it really shouldn't be, for my kid or any other kid in the class.
And 2) if you want half a page on a particular problem, and you want it done a certain way, then you need to either 1) make sure that the kid knows what's expected or 2) make sure there are instructions. My kid is bright, but he's 7. He can do the math, but he can't tell me what to do with his homework. I don't think that's a little kid's failing - I think it's a poor teaching method.
I do think the school is somewhat at fault (not the teacher, because it's a grade-wide problem with kids in other classes too), and we put a lot of time and energy into supplementing his education. I just wish they would assign meaningful, appropriate, engaging work. Homework isn't fun for any of us. But it could be, if only...
Homework is done at home, if it's too easy, make it harder yourself! In fact have him make it harder! I don't think you can expect the teacher to differentiate homework. That is asking way too much!
Ok, I'm the OP here and I really was not expecting this to go to 3 pages.
I don't care about the merits of writing out steps vs doing it in your head. I can see the benefits of dividing work into stages, just as I can see the advantage of being able to work quickly in your head for basic operations.
What I do care about is
1) the work, both reading and math, is ridiculously easy. It's below grade level and it really shouldn't be, for my kid or any other kid in the class.
And 2) if you want half a page on a particular problem, and you want it done a certain way, then you need to either 1) make sure that the kid knows what's expected or 2) make sure there are instructions. My kid is bright, but he's 7. He can do the math, but he can't tell me what to do with his homework. I don't think that's a little kid's failing - I think it's a poor teaching method.
I do think the school is somewhat at fault (not the teacher, because it's a grade-wide problem with kids in other classes too), and we put a lot of time and energy into supplementing his education. I just wish they would assign meaningful, appropriate, engaging work. Homework isn't fun for any of us. But it could be, if only...
Does there have to be one specific way? Maybe the teacher wanted the students to pick their own method, and just explain how they solved it, the steps they took.
Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
Lol, talk about making kids hate math from an early age. Holy shit.
Why would kids hate this more? The point is for the STUDENTS to come up with the strategies...I gave you examples of ways that students can solve addition problems, I just gave them 'names'. It allows kids to use strategies that make sense to them, it means that there isn't just 'one way' to answer questions, there are many ways, which gives value to the thinking of MORE students. There is a lot of research to support the idea that using these kinds of methods make more students feel successful at math.
Homework can be such a conundrum for teachers. Have you thought about the children in school who go home and no one helps them because they are drunk, or on drugs? What about the kid in class who goes home and there is no food, how do they do their homework when they are hungry? Then you have parents like you who are never happy, it's too easy, it's too hard. This is why I'm against homework in the primary grades. You can never win!
Homework is done at home, if it's too easy, make it harder yourself! I fact have him make it harder! I don't think you can expect the teacher to differentiate homework. That is asking way too much!
Ok, so as a teacher, you would be fine with me returning the homework log saying "didn't do the math worksheet because it was unclear and the problems were too easy, did multiplication and counting by 6s instead. Didn't read assigned book for 20 min, because it took 90 seconds, read Percy Jackson novel for 45 minutes instead"?
You wouldn't think I was totally obnoxious and the most difficult parent ever if I did this?
I've always thought that we needed to do the assigned homework, even when it was clearly not appropriate, followed by the additional/supplemental stuff.
also, on a separate issue: he has a differentiated education plan - differentiated homework is exactly what the school board here says he's supposed to get!
I could kiss you. With one post, I finally understand the last entire year of my kid's math. I had no idea how to help her and have been begging her school to provide a parents' tutorial for it. It makes sense, I've used all those strategies for the last 35 years and never knew they were "a real thing. "
Homework is done at home, if it's too easy, make it harder yourself! I fact have him make it harder! I don't think you can expect the teacher to differentiate homework. That is asking way too much!
Ok, so as a teacher, you would be fine with me returning the homework log saying "didn't do the math worksheet because it was unclear and the problems were too easy, did multiplication and counting by 6s instead. Didn't read assigned book for 20 min, because it took 90 seconds, read Percy Jackson novel for 45 minutes instead"?
You wouldn't think I was totally obnoxious and the most difficult parent ever if I did this?
I've always thought that we needed to do the assigned homework, even when it was clearly not appropriate, followed by the additional/supplemental stuff.
also, on a separate issue: he has a differentiated education plan - differentiated homework is exactly what the school board here says he's supposed to get!
Dude I don't even look at the homework kids turn in. I check to see IF they turn it in, I don't check the work. It does nothing to inform my instruction in the classroom, because I wasn't there when it was done. Another argument for not having homework in the primary grades.
rugbywife - will you marry me? i'm so hot for you right now.
lol. It just happens that I spent 2 hours this morning in a PD session directed at math leadership for administrators. Mathematics instruction in the number 1 focus for our board right now so I happen to have JUST spent time learning about this.
I could kiss you. With one post, I finally understand the last entire year of my kid's math. I had no idea how to help her and have been begging her school to provide a parent's tutorial for. I makes sense, I've used all those strategies for the last 35 years and never knew they were "a real thing. "
I can do the subtraction, multiplication and division ones for you too if you want. I did a whole series on this last year when I was still teaching and I learned SOOOOOO much about being more open about my instruction. I ended up teaching by using problems and asking students to explain how they solved the problems, from there we would 'name' strategies and then students would practice using strategies they were unfamiliar with.
I can do the subtraction, multiplication and division ones for you too if you want. I did a whole series on this last year when I was still teaching and I learned SOOOOOO much about being more open about my instruction. I ended up teaching by using problems and asking students to explain how they solved the problems, from there we would 'name' strategies and then students would practice using strategies they were unfamiliar with.
Do you have a document already prepared that explains it? It would be great if you have something you could cut and paste or even email to me. But don't go to the trouble of typing up a huge explanation just for me.
Homework is done at home, if it's too easy, make it harder yourself! I fact have him make it harder! I don't think you can expect the teacher to differentiate homework. That is asking way too much!
Ok, so as a teacher, you would be fine with me returning the homework log saying "didn't do the math worksheet because it was unclear and the problems were too easy, did multiplication and counting by 6s instead. Didn't read assigned book for 20 min, because it took 90 seconds, read Percy Jackson novel for 45 minutes instead"?
You wouldn't think I was totally obnoxious and the most difficult parent ever if I did this?
I've always thought that we needed to do the assigned homework, even when it was clearly not appropriate, followed by the additional/supplemental stuff.
also, on a separate issue: he has a differentiated education plan - differentiated homework is exactly what the school board here says he's supposed to get!
Would you have time to provide an alternate, challenging assignment as well as complete the regular assignment? I meanyeah, in a perfect world, your kid would get what he needed from homework. But would it be possible to take 15 minutes to complete the math worksheet and then say 15 minutes on a fun multiplication website? and then 90 seconds to read the assigned book and 45 minutes of Percy Jackson? Just doesn't seem like it has to be either/or, you know?
Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
I don't understand why you would want to do all this necessary subtraction rather than simply adding. It honestly makes no sense to me and seems to be making things unnecessarily complicated.
And I was a champ at showing my work when I was in school b/c if you fucked it up, you could still get partial credit, so I get the concept, but for adding two digit numbers? I stacked them and added them together, I mean, what more is there to say?
God, I am glad I'm not having kids. I LOVE math and trying to help with this stuff would kill me.
Ok, so as a teacher, you would be fine with me returning the homework log saying "didn't do the math worksheet because it was unclear and the problems were too easy, did multiplication and counting by 6s instead. Didn't read assigned book for 20 min, because it took 90 seconds, read Percy Jackson novel for 45 minutes instead"?
You wouldn't think I was totally obnoxious and the most difficult parent ever if I did this?
I've always thought that we needed to do the assigned homework, even when it was clearly not appropriate, followed by the additional/supplemental stuff.
also, on a separate issue: he has a differentiated education plan - differentiated homework is exactly what the school board here says he's supposed to get!
Dude I don't even look at the homework kids turn in. I check to see IF they turn it in, I don't check the work. It does nothing to inform my instruction in the classroom, because I wasn't there when it was done. Another argument for not having homework in the primary grades.
As a teacher, this is aggravating. Even if I was grading for participation, I always looked at what the students wrote, and made comments. Even with math, you can see the answer, and look at the work to see where they went wrong, right?
As a parent, it's infuriating. If my kid were assigned homework and I knew they spent even ninety seconds on it when that shit wasn't going to get a second glance, heads would roll.
I can do the subtraction, multiplication and division ones for you too if you want. I did a whole series on this last year when I was still teaching and I learned SOOOOOO much about being more open about my instruction. I ended up teaching by using problems and asking students to explain how they solved the problems, from there we would 'name' strategies and then students would practice using strategies they were unfamiliar with.
Do you have a document already prepared that explains it? It would be great if you have something you could cut and paste or even email to me. But don't go to the trouble of typing up a huge explanation just for me.
Thanks!
I might from my grade 5s last year, I can check tomorrow!
i personally think you are making excuses for him. i mean, you are really going to say that this work isn't meaningful? isn't appropriate?
you honestly sound like part of the problem. it's not up to you to decide what parts of the curriculum are important. if it is, then you have the option to homeschool.
Why thank you. But no. In 5 weeks of school, today was the first day we've had a math worksheet (we have never seen a workbook). It included a sentence problem, with a very basic math problem that was less challenging than the work they were doing in grade 1. Is that inappropriate? Yes, it is inappropriate, according to my state's curriculum guidelines.
The kid is bored and doesn't always pay attention. Should he? Of course, but he didn't, and we got work home that is 1) too easy in terms of the actual math, and 2) requires some sort of additional response, with no instructions for me to use when working with him.
we don't actually know what he's supposed to do with those lines on his worksheet. It's entirely speculation. Why? Because there is no explanation. For all we know, he's supposed to diagram the numbers in color. So you're making some pretty big presumptions right there.
I'm trying to navigate homework that my kid doesn't want yo do because he's bored and frustrated to be getting work below the level of last year's end of grade assignments. I wish he was more motivated and attentive, but, honestly, I understand why he's not. I'm also trying to work with the teacher and not sabotage by assigning more challenging materials. But it's really difficult when they send home books and math below grade level, and when the specifics of the assignment don't get explained clearly on the work itself.
Dude I don't even look at the homework kids turn in. I check to see IF they turn it in, I don't check the work. It does nothing to inform my instruction in the classroom, because I wasn't there when it was done. Another argument for not having homework in the primary grades.
As a teacher, this is aggravating. Even if I was grading for participation, I always looked at what the students wrote, and made comments. Even with math, you can see the answer, and look at the work to see where they went wrong, right?
As a parent, it's infuriating. If my kid were assigned homework and I knew they spent even ninety seconds on it when that shit wasn't going to get a second glance, heads would roll.
It's second grade. How on earth is homework going to inform my instruction other than who is doing it and who is not? We don't give grades for homework, not even participation grades. I'm also not going to waste my time going over homework, when can use that time to look at in class work, make small groups and create teaching points from work that actually informs my instruction.
Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
I don't understand why you would want to do all this necessary subtraction rather than simply adding. It honestly makes no sense to me and seems to be making things unnecessarily complicated.
And I was a champ at showing my work when I was in school b/c if you fucked it up, you could still get partial credit, so I get the concept, but for adding two digit numbers? I stacked them and added them together, I mean, what more is there to say?
God, I am glad I'm not having kids. I LOVE math and trying to help with this stuff would kill me.
It makes no sense to you but it makes sense to some kids...and that's what matters...if their strategy shows strong NUMBER SENSE, and helps them arrive at the right answer, it is a meaningful strategy. Being able to see where to subtract in order to add more easily shows greater knowledge and understanding of numbers and their value than simple stacking does.
Okay, traditional algorithm - explanation: I stacked the numbers, first I added the numbers in the one column, carried the one and added it to the sum of the numbers in the tens column. My answer was 112.
56 +56 112
Breaking numbers apart into tens and ones - explanation: I split the tens from the ones, so first I add the tens (50+50=100) and then I added the ones (6+6=12) and then I added those two together to get 112.
Friendly/Compatible numbers: I know I can add 55+55 and get 110. I know I still have 2 left to add because I subtracted 1 from each number to start. So I get 110 plus 2, which is 112.
Counting on by 10s: I start at 56 and at 10, to 66, add 10, to 76, add 10, to 86, add 10 to 98, add 10, to 106 and then add 6 more to get 112.
There's 4 ways, there are more but some strategies work better with some numbers than others.
For example...
98+75 - using the traditional algorithm works here but compensation works better:
I make 98 into 100 because it is easier to add to 100. That means I need to subtract 2 from 75, giving me 73. I can add 100 to 73 in my head and get 173.
I don't understand why you would want to do all this necessary subtraction rather than simply adding. It honestly makes no sense to me and seems to be making things unnecessarily complicated.
And I was a champ at showing my work when I was in school b/c if you fucked it up, you could still get partial credit, so I get the concept, but for adding two digit numbers? I stacked them and added them together, I mean, what more is there to say?
God, I am glad I'm not having kids. I LOVE math and trying to help with this stuff would kill me.
Because not everyone understands concepts the same exact way you do. YWIA. EWCM.
Post by sparkythelawyer on Sept 30, 2013 20:12:16 GMT -5
Never fear, Joenali's here to tell us all that teachers are fabulous and parents should just shut up and know how hard teachers have it and how right they are in everything they do....
I don't understand why you would want to do all this necessary subtraction rather than simply adding. It honestly makes no sense to me and seems to be making things unnecessarily complicated.
And I was a champ at showing my work when I was in school b/c if you fucked it up, you could still get partial credit, so I get the concept, but for adding two digit numbers? I stacked them and added them together, I mean, what more is there to say?
God, I am glad I'm not having kids. I LOVE math and trying to help with this stuff would kill me.
It makes no sense to you but it makes sense to some kids...and that's what matters...if their strategy shows strong NUMBER SENSE, and helps them arrive at the right answer, it is a meaningful strategy. Being able to see where to subtract in order to add more easily shows greater knowledge and understanding of numbers and their value than simple stacking does.
Huh. Thanks. I wasn't trying to be a bitch - this is the way I was taught in the olden days, so I really did not understand. I like to keep things as simple as possible. But dude, without your prior explanation, if my imaginary kid brought home homework that did not involve stacking, I would have no clue how to help.
Post by juliahenry on Sept 30, 2013 20:14:19 GMT -5
Also, thanks rugbywife. That's a helpful explanation of why/how ds does math the way he does.
He's doing the techniques. He's perfectly capable of the work, but I still think the homework sheet tonight was challenging for reasons unrelated to the math.
Never fear, Joenali's here to tell us all that teachers are fabulous and parents should just shut up and know how hard teachers have it and how right they are in everything they do....
Hmmm, that's not what I'm saying!! I'm saying that she can make homework harder, it's work done at home. I'm also saying that she should take a look at the standards, I'm also saying that homework should not be given in the primary grades for many of the reasons the op is complaining about. Why are you such a twat?
It makes no sense to you but it makes sense to some kids...and that's what matters...if their strategy shows strong NUMBER SENSE, and helps them arrive at the right answer, it is a meaningful strategy. Being able to see where to subtract in order to add more easily shows greater knowledge and understanding of numbers and their value than simple stacking does.
Huh. Thanks. I wasn't trying to be a bitch - this is the way I was taught in the olden days, so I really did not understand. I like to keep things as simple as possible. But dude, without your prior explanation, if my imaginary kid brought home homework that did not involve stacking, I would have no clue how to help.
Addition isn't really the best example for this, multiplication is. A lot of parents have their kids 'learn' their multiplication tables...the thing is, they can memorize the 'facts' but that doesn't mean they understand the actual concept of what multiplication MEANS in terms of what is happening to the numbers.
So a student might be able to stack two two-digit numbers and perform a multiplication using a traditional algorithm but that doesn't mean they will understand what they are doing when they perform the multiplication, they don't understand that they are making 13 groups of 13...so, if they make an error in their work, and end up with a number that is, let's say, less than 100, they can't look at their work and realize that it can't possibly be less than 100 because 10 groups of 10 would be 100 so 13 groups of 13 has to be more than 100.
Where you really see the gaps in mathematical understanding in multiplication is when you arrive at division word problems. There are two types of division questions, partitive and quotative. Doing standard division algorithms doesn't allow for the distinction between partitive and quotative questions, which is what is needed in order to conceptually understand division word problems.
My son is in 5th grade and, just the other day, had to do a math homework sheet where he was to explain how to get the answer. He wrote "use a calculator". I had him change it, but I admit that I did get a good laugh out of that.
Never fear, Joenali's here to tell us all that teachers are fabulous and parents should just shut up and know how hard teachers have it and how right they are in everything they do....
Hmmm, that's not what I'm saying!! I'm saying that she can make homework harder, it's work done at home. I'm also saying that she should take a look at the standards, I'm also saying that homework should not be given in the primary grades for many of the reasons the op is complaining about. Why are you such a twat?
Many here would tell you I was born this way :-)
I have yet to see you take a parents side on these posts. There is usually a whole lot of variance between "We teachers live and bleed for our students! We do so much! You should lay off of that poor teacher" and "Why should a teacher have to stop and answer your question, parent? We don't have time to do such things."
I do not tend to see you take a moment to think about how a situation might look to a parent, and it makes me feel like you are not really concerned with what the parents think or what their concerns are.