• # Elementary Mathematics Grade 5 Unit 1

Subject: Mathematics
Timeline: 9 days
Unit 1 Title: Place Value and Base Ten

Unit Overview:

This unit will give the opportunity for students to practice, review, and develop strategies for identifying, preparing and ordering place value in whole and decimal numbers.  The students will be engaged in activities to learn various notations of multi-digit whole and decimal numbers.  The unit will also provide and introduction to place value using powers of ten.

Unit Objectives:

At the end of this unit, all 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 multi-digit whole and decimal numbers in standard, word, and expanded form.  All students must understand the relationship between place value and powers of ten.

Focus Standards:

PA.CCSS.Math.Content.CC.2.1.5.B.1  Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. (5.NBT.1, 5.NBT.2, 5.NBT.3)
PA.CCSS.Math.Content.CC.2.1.5.B.2  Extend an understanding of operations with whole numbers to perform operations including decimals. (5.NBT.7)
PA.CCSS.Math.Content.CC.2.4.5.A.1  Solve problems using conversions within a given measurement system. (5.MD.1)

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 jumping into a solution attempt. They monitor and evaluate their pathway and change course if necessary. Mathematically proficient students check their answers to problems using a different method and continually ask themselves, “Does this make sense?”

#2 Reason Abstractly and Quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complimentary abilities to bear on problems involving quantitative relationships: the ability to decontextualize and the ability to contextualize. Quantitative reasoning entails habits of creating 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.

#3 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.

#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.

#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, or a calculator. Proficient students are sufficiently familiar with tools appropriate for their grade 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 use clear definitions in discussion with others and in their own reasoning. They are careful about specifying units of measure, specifying axes and use careful calculations.

#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.

#8 Look for and express regularity and 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. 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.

Concepts - Students will know:
• How to compare and order whole and decimal numbers
• How to note decimals in standard and expanded form
• That place value is related to powers of 10
Competencies -Students will be able to:
• Compare decimal numbers
• Order decimal numbers
• Write decimals in standard form
• Write decimals in expanded form
• Make larger numbers by multiplying by 10

Assessments:
• Unit 1 Assessment
• Daily RSA

Elements of Instruction:

This unit will continue to build understanding of decimal numbers.  In fourth grade, students were introduced to the concept that decimals can be compared to fractions.  They were also taught that decimals and fractions can change forms between themselves.  Students were also given the opportunity to add and subtract decimals.  In fifth grade, students begin to really unpack the place value chart to include decimal numbers.

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