Curriculum Standards

 Grade 5 Standards   Each student will ……………….        Use a variety of 	strategies in the problem-solving process   Use a variety of strategies to understand problem situations (e.g., discussing with peers, stating problems in own words, 		modeling problem with diagrams or physical objects, identifying a 		pattern)</li> <li class="MsoNormal">Represent problems situations in a variety of 		forms (e.g., translates from a diagram to a number or symbolic 		expression)</li> <li class="MsoNormal">Understand that some ways of representing a 		problem are more helpful than others</li> <li class="MsoNormal">Use trial and error and the process of elimination to solve problems</li> <li class="MsoNormal">  Know the difference between pertinent and irrelevant information when solving problems </a></li> <li class="MsoNormal">Understand the basic language of logic in 		mathematical situations (e.g., &quot;and,&quot; &quot;or,&quot; &quot;not&quot;)</li> <li class="MsoNormal">Use explanations of the methods and reasoning behind the problem solution to determine reasonableness of and to verify results with respect to the original problem</li> <li class="MsoNormal">Understand basic valid and invalid arguments (e.g., counter examples, irrelevant approaches)</li> </ol> </li> </ol> <p class="MsoNormal" style="margin-left:.75in"> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="2" type="1"> <li class="MsoNormal">Understand and apply basic and advanced properties of the concepts of numbers</b> <ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A"> <li class="MsoNormal">Apply the basic meaning of place value</li> <li class="MsoNormal">Relate the relative magnitude among whole numbers, fractions, decimals, and mixed numbers</li> <li class="MsoNormal">Use models (e.g., number lines, two-dimensional 		and three-dimensional regions) to identify, order, and compare numbers</li> <li class="MsoNormal">Understand the relationships among equivalent number representations (e.g., whole numbers, positive and negative 		integers, fractions, ratios, decimals, percents, scientific notation, 		exponentials) and the advantages and disadvantages of each type of 		representation</li> </ol> </li> </ol> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="3" type="1"> <li class="MsoNormal">Use basic and advanced procedures while performing the processes of computation</b> <ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A"> <li class="MsoNormal">  Solve real-world problems involving number operations (e.g., computations with dollars 		and cents) </a></li> <li class="MsoNormal">Apply the language of basic operations (e.g., 		&quot;products,&quot; &quot;multiplication&quot;)</li> <li class="MsoNormal">Add, subtract, multiply, and divide integers, and rational numbers</li> <li class="MsoNormal">Add and subtract fractions with unlike denominators; multiples fractions</li> </ol> </li> </ol> <p class="MsoNormal" style="margin-left:.75in"> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="4" type="1"> <li class="MsoNormal">Understand and apply basic and advanced properties of the concepts of measurement</b> <ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A"> <li class="MsoNormal">Know approximate size of basic standard units (e.g., centimeters, feet, grams) and relationships between them (e.g., 		between inches and feet</li>		<li class="MsoNormal">Understand relationships between measures (e.g., between length, perimeter, and area)</li>		<li class="MsoNormal">Understand that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times)</li>		<li class="MsoNormal">Use specific strategies to estimate quantities and 		measurements (e.g., estimating the whole by estimating the parts)</li>		<li class="MsoNormal">Select and uses appropriate units of measurement, 		according to type and size of unit</li>	</ol>	</li> </ol> <p class="MsoNormal" style="margin-left:.25in"> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="5" type="1">	<li class="MsoNormal">Understand and apply basic and advanced properties 	of the concepts of geometry</b> 	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A">		<li class="MsoNormal">Use geometric methods (i.e., an unmarked straightedge and a compass using an algorithm) to complete basic 		geometric constructions (e.g., copying sides and angles).</li>		<li class="MsoNormal">Use motion geometry (e.g., turns, flips, slides) 		to understand geometric relationships</li>		<li class="MsoNormal">Apply characteristics of lines (e.g., parallel, perpendicular, intersecting), angles (e.g., right, acute, vertical, adjacent) and polygons (types of triangles)</li>	</ol>	</li> </ol> <p class="MsoNormal" style="margin-left:.75in"> <p class="MsoNormal" style="margin-left:.75in"> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="6" type="1">	<li class="MsoNormal">Understand and apply basic and advanced concepts of 	statistics and data analysis</b> 	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A">		<li class="MsoNormal">Organize and display data in simple bar graphs, 		pie charts, and line graphs</li>		<li class="MsoNormal">Read and interpret simple bar graphs, pie charts, 		and line graphs</li>		<li class="MsoNormal">Understand that data come in many different forms 		and that collecting, organizing, and displaying data can be done in many 		ways</li>		<li class="MsoNormal">Understand the basic concept of a sample (e.g., a 		large sample leads to more reliable information; a small part of 		something may have unique characteristics but not be an accurate representation of the whole)</li>		<li class="MsoNormal">Calculate measures of central tendency (i.e., mean, mode, median)</li>	</ol>	</li> </ol> <p class="MsoNormal" style="margin-left:.25in"> <ol style="margin-top: 0in; margin-bottom: 0in" start="7" type="1">	<li class="MsoNormal">Understand and apply basic and advanced concepts in 	probability.</b> 	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A">		<li class="MsoNormal">Recognize events that are sure to happen, events 		that are sure not to happen, and events that may or may not happen 		(e.g., in terms of &quot;certain,&quot; &quot;uncertain,&quot; &quot;likely,&quot; &quot;unlikely&quot;)</li>		<li class="MsoNormal">Understand that statistical predictions are better 		for describing what proportion of a group will experience something 		(e.g., what proportion of automobiles will be involved in accidents) 		rather than which individuals within the group will experience 		something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur</li>		<li class="MsoNormal">Use basic sample spaces (i.e., the set of all possible outcomes) to describe and predict events</li>		<li class="MsoNormal">Determine probability using 		mathematical/theoretical models (e.g., table or tree diagram, area model, list, sample space)</li>		<li class="MsoNormal">Determine probability using simulations or 		experiments</li>	</ol>	</li> </ol> <p class="MsoNormal"> <p class="MsoNormal">  <p class="MsoNormal">  <ol style="margin-top: 0in; margin-bottom: 0in" start="8" type="1">	<li class="MsoNormal">Understand and apply basic and advanced properties 	of functions and algebra</b> 	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A">		<li class="MsoNormal">Recognize that a variable is a letter or symbol 		that stands for one or more numbers</li>		<li class="MsoNormal">Understand the basic concept of an equality 		relationship (i.e., an equation is a number sentence that shows two quantities that are equal)</li>		<li class="MsoNormal">Solve simple open sentences involving operations 		on whole numbers (e.g., ? + 17 = 23)</li>		<li class="MsoNormal">Apply basic understanding of characteristics and 		features of the rectangular coordinate system (e.g., the horizontal axis is the X axis and the vertical axis is the Y axis)</li>		<li class="MsoNormal">Know that an expression is a mathematical 		statement using numbers and symbols to represent relationships and 		real-world situations (e.g., equations and inequalities with or without variables)</li>	</ol>	</li> </ol> <p class="MsoNormal"> <p class="MsoNormal"> <p class="MsoNormal"> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="9" type="1">	<li class="MsoNormal">Understand the general nature and uses of 	mathematics</b> 	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A">		<li class="MsoNormal">Understand that numbers and the operations 		performed on them can be used to describe things in the real world and 		predict what might occur</li>		<li class="MsoNormal">Understand that mathematical ideas and concepts 		can be represented concretely, graphically, and symbolically</li>	</ol>	</li> </ol> <p class="MsoNormal"> <ol style="margin-top: 0in; margin-bottom: 0in" start="10" type="1">	<li class="MsoNormal">Use technology tools to enhance learning and 	productivity. </b>	<ol style="margin-top: 0in; margin-bottom: 0in" start="1" type="A"> <li class="MsoNormal">Use a calculator to compute and verify mathematical operations.</li> <li class="MsoNormal">Use computer applications (such as MS Excel or 		Inspiration) to produce tables, charts and/or graphs) </li>	</ol>	</li> </ol> <p class="MsoNormal">