The following are two examples of students using different strategies to show how they arrived at their answers.
Understanding a problem is much more important than simply getting the correct answer. This statement definitely applies to fractions, a topic that can even get us adults confused at times. I ask my students to prove their answers by drawing pictures, using number lines, or decomposing. Students may also use words to explain their thinking. I understand that the process of explaining ones' work is not the way we learned growing up, where the emphasis was on answering as many questions as possible instead of actually understanding why the process worked; however, if your child really understands a skill or concept and does not just learn tricks to help get the answer easily, he/she will be a much better thinker and reasoner, and will do much better down the road when problems (and school in general) becomes more and more complicated. The following are two examples of students using different strategies to show how they arrived at their answers. With the above being said, I am not saying tricks and shortcuts do not have a place in fourth grade. I only mean to say that these tricks should not be taught at first; it would mean so much more to the student if they could discover the tricks themselves! Tricks do not help students learn and comprehend the process or skills that are being taught. Once students are taught a shortcut, they tune me out completely because they have an easy way to find the answers. Students who are only taught tricks and who do not understand why those tricks work will not do well in my class or down the road when math becomes more challenging.
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Students did a great job representing our school today! We got to see "The Wizard of Oz." It was a a really cute play! Student should connect this new skill to what they learned about multiplication in third grade. To multiply means to have "equal groups of". Take the following problem for example: If Mrs. Dabney uses 1/4 cups of sugar in a gallon of sweet tea, how many cups would she use in 6 gallons? This problem could be solved a variety of ways. Students could think of their fraction strips and sketch the problem or write 6 groups of 1/4, as shown below: Students can write the equation as an addition sentence (pictured above) or as 6 x 1/4 = 6/4. Students should understand that the denominator does not change when you are adding fractions with like denominators or multiplying fractions by a whole number because the size of the pieces does not change. An awesome math specialist came to our first block class today and taught the lesson. It was nice to switch it up, and I learned a lot from watching her teach. My students made me super proud of both their behavior and their answering of her questions. Students used their fraction strips, pattern blocks, pictures, number lines, and symbols (numbers) to solve several problems like the example above. It is incredibly important that students understand conceptually how to solve fraction problems, not just be taught a trick (like using cross multiplication for finding equivalent fractions). Students must be able to explain how they found their answer by drawing pictures and using words. This is a skill students will need to practice, practice, practice! Students should always have their homework. We have math homework each and every night. When students do not have their homework they must fill out a "homework excuse note". These are always attached to their work reports so parents will be aware of missed assignments. A popular excuse from students is either that they forgot or that they lost it. These excuses are in no way acceptable, and in the video below, Kanzata demonstrates exactly why. At the beginning of the year, students were provided with a homework folder, and in that folder are several page protectors where certain papers should be placed. This includes our weekly newsletter, math and science study guides, and tonight's math homework. If students will take the extra 20 seconds to put their homework where it goes, they should never have to write on their excuse note "I lost it." Great job, Kanzata and several other students who take time each and every day to make sure they always put their papers in the appropriate place! You guys rock! OK, not really, but what better way to learn about fractions?! Students worked with a partner to create their own story problems involving two different types of pizza cut into eighths. A few students volunteered to share their problems with the rest of the class. Today we discussed and practiced several ways to solve addition and subtraction problems involving fractions:
I was really impressed with how quickly students picked up these new skills! They are doing a GREAT job with fractions! Today many students were still confused by how to use fraction strips to find equivalent fractions, so those students having mastered this skill stepped up and helped teach their peers! Students were performing much better by the end of the lesson, and a few even told me that they were able to figure out where they were making their mistake or getting confused. Impressive! Two incorrect answers given on student papers yesterday read: 2/3 = 6/12 and 2/3 = 2/6 I asked students to think about what they know about fractions to explain how one can tell that 2/3 does not equal 6/12 and that 2/3 does not equal 2/6. Two examples of explanations are below: Why 2/3 does not equal 6/12Why 2/3 does not equal 2/6Today students practiced classifying animals by sorting them first into two groups, vertebrates and invertebrates, then further into the five different vertebrate groups: reptiles, fish, birds, amphibians, and mammals. There were a few tricky animals, like sting rays and sea horses (both belonging in the fish group) as well as dolphins (mammal) but for the most part, students did a great job! We started our movie maker project today! This is an exciting project on which students will spend the next 8-10 weeks working. Last week students chose a biome they wished to learn more about. Today they began doing research on that biome so they can become "experts". Below is a clip of students working...I also asked a few students to share some interesting facts they learned while researching their biomes. Students may use a variety of strategies to find equivalent fractions. We noticed today that having a model makes finding equivalent fractions pretty easy! Students can use their fraction strips or draw pictures. Two students volunteered to show how each strategy works: Using Fraction STripsDrawing a modelWhile there is another strategy, multiplying both the numerator and denominator by the same number, students should not be taught or use this strategy until they understand it fully and can explain why it works. By having multiple experiences using strips and drawing models, students will hopefully start to see patterns and begin to make generalizations about finding equivalent fractions.
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