Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order

Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
Modelling and Ordering Decimals and Fractions on a Number Line - Shade and Order
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This bundle includes five sheets that will challenge your students to model fractions and decimals, place them on a number line, then write them in order. Students will explore multiple ways to write and conceptualize decimals and fractions so they understand WHY they go in the order that they do.

Viewing decimals and fractions in multiple contexts gives students a deeper understanding of what these numbers actually represent. Each sheet explores one set of four decimal numbers and fractions that students must represent in multiple ways. Answer keys included.

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Keywords: fractions, decimals, decimal numbers, math, addition, adding decimals, modeling decimals, decimal concepts, tenths, rounding, decimal number lines, rounding decimals, ordering decimals, ordering fractions, converting fractions to decimals, converting decimals to fractions

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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)/(π‘₯ – 1) = 3. Noticing the regularity in the way terms cancel when expanding (π‘₯ – 1)(π‘₯ + 1), (π‘₯ – 1)(π‘₯Β² + π‘₯ + 1), and (π‘₯ – 1)(π‘₯Β³ + π‘₯Β² + π‘₯ + 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.
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 Γ— 8 equals the well remembered 7 Γ— 5 + 7 Γ— 3, in preparation for learning about the distributive property. In the expression π‘₯Β² + 9π‘₯ + 14, older students can see the 14 as 2 Γ— 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(π‘₯ – 𝑦)Β² 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 π‘₯ and 𝑦.
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.
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.
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.
Total Pages
10 pages
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Included
Teaching Duration
N/A
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