• # Elementary Mathematics Grade 5 Introductory Unit

Subject: Mathematics
Timeline:  10 Days
Unit Title: Introductory Unit

Unit Overview:

This unit will give students the opportunity to review and practice the Common Core Skills taught in the fourth grade lessons in the areas of place value, geometry, measurement, whole and decimal fraction computation, and factors and multiples.  The students will also be engaged in activities that review important fourth grade academic vocabulary.

Unit Objectives:

At the end of this unit, the students must be able to demonstrate knowledge of identifying, comparing, and ordering place value in whole and decimal numbers.  Students must be able to notate numbers in standard, word, and expanded forms.  Students must be able to demonstrate knowledge of addition and subtraction strategies, multiplication and division strategies, and have a basic understanding of not only decomposing fractions, but adding and subtracting fractions as well.  Students must be able to identify and classify quadrilaterals, triangles, and angles, convert Customary and Metric units of measurement, use a protractor to measure angles, and find factors and multiples of numbers.

Focus Standards:

PA.CCSS.Math.Content.CC.2.1.4.C.1  Extend the understanding of fractions to show equivalence and ordering. (4.NF.1, 4.NF.2)
PA.CCSS.Math.Content.CC.2.1.4.C.2   Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (4.NF.3, 4.NF.4)
PA.CCSS.Math.Content.CC.2.1.4.C.3 Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). (4.NF.5, 4.NF.6)
PA.CCSS.Math.Content.CC.2.4.4.A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. (4.MD.1, 4.MD.2)
PA.CCSS.Math.Content.CC.2.4.4.A.6 Measure angles and use properties of adjacent angles to solve problems. (4.MD.6)
PA.CCSS.Math.Content.CC.2.1.4.B.1 Apply place value concepts to show an understanding of multi-digit whole numbers. (4.NBT.1, 4.NBT.2, 4.NBT.3)
PA.CCSS.Math.Content.CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.4, 4.NBT.5, 4.NBT.6)
PA.CCSS.Math.Content.CC.2.4.4.6.A.6 Draw lines and angles and identify these in two- dimensional figures. (4.G.1)
PA.CCSS.Math.Content.CC.2.2.4.A.2 Develop and/or apply number theory concepts to find factors and multiples. (4.OA.4)

Mathematical Practice Standards:

#1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

#2 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.

#4 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. 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.

#5 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.
#6 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.

#7 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 * 8 equals the well-remembered 7 * 5 + 7 * 3, in preparation for learning about the distributive property.

Concepts - Students will know:
• How to use place value to order and compare numbers
• Standard Form
• Expanded Form
• Strategies for addition, subtraction, multiplication, and division
• Fractions sets, regions, and fractions
• Operations with fractions
• Geometric Properties
Competencies -Students will be able to:
• Compare numbers
• Write numbers in standard form
• Write numbers in expanded form
• Add, subtract, multiply, and divide multi-digit numbers
• Solve fractions of sets, regions, and fractions
• Describe geometric properties of various polygons

Assessments:
• None

Elements of Instruction:

This unit is a collection of the basic concepts that were taught in fourth grade.  Students should have a basic understanding of all that is asked of them during this comprehension unit.

Differentiation:

Each lesson has differentiation options for each portion of the lesson.  Additional differentiation options are listed with directions and student masters in the Teacher’s Guide to Games.

Interdisciplinary Connections:
• Mental Math and Math message