Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000

Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
Number Sense with Number Lines! Deepening Place Value Understanding to 1,000,000
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  1. Using number lines to develop a solid understanding of number sense and place value is absolutely critical as we move our students forward in their mathematical thinking. This is true for fractions and decimals too! We often expose students to numbers in a variety of ways…using manipulatives, using
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Why number lines? A solid understanding of number sense and place value is absolutely critical as we move our students forward in their mathematical thinking. We often expose them to numbers in a variety of ways…using manipulatives, using 100’s charts, and so on. One area that is often overlooked is the building of understanding of how numbers relate to each other and how they “fit” with other numbers.

For example…students may have a solid understanding of what “10” is and how to model it—but they don’t always realize what “10” means compared to other numbers…that 10 is half of 20…and double 5…and closer to 0 than to 100 and so on! In my attempt to really help my students understand place value AND develop their mathematical practices, I have developed these resources and share them with you now! THIS edition focuses on numbers through ONE MILLION.

What is included?

This resource has a number of different elements to help you tackle place value--including 8 pages of information, teaching tips, and photos of the resource in action!

It includes 65 ready-to-copy math journal problems (5 per page) that ask students to either identify a mark on a number line or to make a mark at a certain point on a number line. These are NOT meant to be exact answers—but for students to use their number sense to come up with reasonable solutions. What is CRITICAL is the second part—”Explain your thinking!” Whether students work together or alone, the problems ask them to defend their solutions. There are problems at a variety of levels…you will notice that they start easier and get more sophisticated—including a set of pages where the number lines do not start at 0. Look through and see which problems are the right level of challenge for your class—and consider differentiating by giving different groups different problems.

Also included is a set of 12 pages that can be used as either homework or assessments! Students are asked to do the same types of problems as used in math journals, but are asked to work on them independently. The pages increase in difficulty as their number increases.

A simple rubric to help you assess how well your students are able to “Construct viable arguments” and a class checklist to record progress.

NOTE: This is a challenging resource geared toward helping grade 4-5 teachers "raise the rigor" of their math instruction. Differentiation tips are included!

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Looking for all my number line resources?

Number Lines to 120

Number Lines to 1,000

Number Lines to 1,000,000

Number Lines with Fractions and Decimals

Number Line Resource BUNDLE of 3 resources (Does not include the number lines to 120 resource)

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All rights reserved by ©The Teacher Studio. Purchase of this problem set entitles the purchaser the right to reproduce the pages in limited quantities for single classroom use only. Duplication for an entire school, an entire school system, or commercial purposes is strictly forbidden without written permission from the author at fourthgradestudio@gmail.com. Additional licenses are available at a reduced price.

Log in to see state-specific standards (only available in the US).
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.
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.
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.
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
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54 pages
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