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Instead, they need targeted instruction that highlights the conceptual understanding of what fractions are, what they look like in various representations, how they relate to other fractional quantities, and why the procedures in the algorithms for adding and subtracting fractions work (Boaler, 2015). . . . #mathteacher #mathteachers #fractions #fractionsarefun #mathcoach #downriverresources #downriveredu #teachersofinstagram #texasteachers #texasteacher #iteachtoo #igconnect4edu #igteacher #iteach5th #iteach4th #iteach3rd #iteach345 #iteach456 #iteachupperelementary
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ADDING FRACTIONS WITH UNLIKE DENOMINATORS // We lose a lot of mathematicians when introducing addends with unlike denominators. Here’s an activity to help keep you afloat! ⤵️ ———————————————————————— ➡️ Focus: 1/2 + 1/4 1️⃣ Ask: Can I add one-half plus one-fourth? 2️⃣ Discuss with your partner. 3️⃣ Share out with the class. Sample answer: “I cannot add 1 half plus 1 fourth until the units are the same. We need to find like units.” 4️⃣ Make like units by folding paper as shown in the photograph above. ———————————————————————— 🗣 What problems do you run into when introducing addends with unlike denominators? . . . . #iteachmath #iteach345 #iteach3rd #iteachthird #iteach4th #iteachfourth #iteach5th #iteachfifth #iteachtoo #texasteachers #teacher #classroomideas #downriverresources #downriveredu #instagramteacher #igteachers #teachersfollowteachers #fractions #fractionsarefun #igconnect4edu #iteach
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Start with Fair Shares // “One fifth is more than one fourth,” the eager student exclaimed. This misconception is common when mathematicians begin to explore fractions. The whole number five is more than four, so why wouldn’t one fifth be more than one fourth? ———————————————————————— In traditional classrooms, fractions are often introduced as a number within quotative contexts (divided into groups— instead of divided evenly). In the early grades, children are often asked to shade in parts of a whole and label them with the appropriate fraction. ———————————————————————— When fractions are treated as numbers in the beginning of the journey—too early on—learners often assume that the greater the denominator, the greater the amount — one-eighth is greater than one-seventh because 8 is greater than 7. ———————————————————————— One of the benefits of starting to explore fractions using a fair-sharing situation, as division, is that this misconception is easily dispelled. ———————————————————————— Creating a shared experience to begin exploring fractions helps all mathematicians addresses this concept. I recommend using the classic text The Doorbell Rang by Pat Hutchins. Each ring of the doorbell brings more friends to share the delicious cookies Ma has made. ———————————————————————— 🗣 Teacher Talk: What misconceptions with fractions have popped up in your classroom? ⤵️
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Mathematicians need opportunities to work with a variety of representations of fractions, not just pizzas and brownies! 🙊 They need to develop a concrete realization of a fraction. ———————————————————————— Just as young mathematicians use counters to help anchor a mental image of a whole number, mathematicians can use number lines to show how a fraction (or decimal or percent) can be inserted between any two fractions. ———————————————————————— Number lines allow comparisons of fractions, decimals, and percentages and also serve as measurement or iteration models for computation. ———————————————————————— 🗣 Teacher Talk: What models do you use for fractions? What models do you want to learn more about? ⤵️ I’m featuring fractions all week long! 👣 here @downriveredu for more!
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🤔 Did you know that? Proficiency with fractions is an important foundation for learning more advanced mathematics. Fractions are a mathematician’s first introduction to abstraction in mathematics and provide the best introduction to algebra in the elementary and middle school years. ———————————————————————— 🖐🏻 Mathematicians need opportunities to work with a variety of representations of fractions, including set and region models. They need to develop a concrete realization of a fraction. ———————————————————————— ⏰ Time and emphasis are necessary for mathematicians to develop the links among fractions, decimals, and percents and solve problems involving their use. ———————————————————————— 🗣 Teacher Talk: What do you want to learn about fractions in this feature? ⤵️
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Tell me: Did you use ten frames as a child? When did you learn about ten frames? I’m curious about your early math experiences! ⤵️ ———————————————————————— ❌ I didn’t use them in school as a child. ❌ I didn’t learn about them in college. ❌ I didn’t learn about them in PD. ❌ I didn’t learn about them from the teacher next door in New Mexico. ✅ I FINALLY first learned about them from another teacher when I began teaching kindergarten in Texas. ⚠️ It is my passion to keep YOU afloat! I believe WE can positively impact students’ math experiences! ———————————————————————— 🙋🏻♀️ If you want to learn more about ten frames, I’ve been sharing about them in this feature. Go back through the last few posts! ———————————————————————— 📸 Differentiated Math Mats {cover 11 numeracy skills for Grades K-2}: https://www.teacherspayteachers.com/Product/Math-Mats-Differentiated-Math-Center-for-Mini-Erasers-Math-Manipulatives-4407055 ———————————————————————— 👣 I’ll be sharing more math all summer long right here! @downriveredu . . . #downriverresources #teachersofinstagram #teachersfollowteachers #targetteachers #sterilitenation #iteachmath #mathteachers #texasteacher #texasteachers #iteachk #kindertribe #iteach1st #iteach2nd #teacherspayteachers #instructionalcoach #guidedmath #mathcenters #iteachtoo #teachertalk #differentiatedinstruction
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⬆️ This is my go-to explanation when teaching how to use a ten frame. We are accustomed to “seeing” numbers on a ten frame this way. ———————————————————————— “Always fill the top row first, starting on the left, the same way you read. When the top row is full, counters can be placed on the bottom row, also from the left. This will produce the standard way to show numbers on the ten-frame, says researcher John Van de Walle. ———————————————————————— 🗣 Teacher Talk: Do you have something standard that you say when teaching ten frames? What is the biggest problem you run into with ten frames? Join the conversation. ⤵️ ———————————————————————— 👣 Follow along @downriverresources as we dive into math topics for home and school of your choosing all summer long! 🌊 . . . #downriverresources #downriveredu #mathcoach #numeracy #tenframes #iteachk #kindertribe #kindergartenteacher #mathteacher #math #teachersofinstagram #teachertalk #iteachtoo #teachersfollowteachers #teacherspayteachers #homeschoolmath #iteachmath #teachingideas
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Who needs a whiteboard when you have a washer? Compose & Decompose Numbers •• WHY USE IT? Being flexible with building and breaking numbers apart helps mathematicians and is an important facet of number sense. Composing and decomposing small sets of objects allows mathematicians to see the whole group as well as the subsets that created the whole. Composing and decomposing numbers makes “friendlier” numbers making computing efficient. ———————————————————————— HERE’S HOW IT WORKS: 1️⃣ The teacher briefly tells the mathematicians to make the number 10 using two addends. Using a ten frame makes this easy as the counters will occupy each space to “fill” the frame. 2️⃣ Mathematicians use red and yellow counters to show the number using a ten frame. Representations will vary: 1 and 9; 2 and 8; 3 and 7; 4 and 6; 5 and 5; 6 and 4; 7 and 3; 8 and 2; 9 and 1. 3️⃣ The teacher prompts students to explain their thinking and justify their reasoning. 4️⃣ The teacher asks mathematicians to generate another way to make 10. ———————————————————————— TEACHER PROMPTS: ⏺ How did you make 10? ⏺ How did you keep track of the quantity? ⏺ How do you know you have found all the ways to decompose this number?” This routine can be used to compose and decompose other numbers too! 😀 ———————————————————————— 🗣 Tell me: What have you used to teach composing and decomposing numbers? ⤵️ ———————————————————————— 💡 Want to learn more math ideas? Follow along this summer! @downriveredu . . . #downriverresources #downriveredu #mathcoach #mathteachers #mathteacher #iteachmath #iteachk #composingnumbers #decomposingnumbers #tenframe #mathtools #teacherspayteachers #distancelearningtpt #iteachtoo #kindertribe #iteachfirst #iteach1st #teachersofinstagram #mathathome #drrmathathome #athomelearning #bettertogether #raedunnteacher
