Bao Xiong & Ashley McLaughlin
MATH Unit: Number Sense - Place Value
Grade: 3rd
Introduction & Overview:
Our unit is Number Sense and Place Value which is geared for 3rd grade. We have
planned enough activities for a two-week or ten day unit. We both have had different
experiences learning mathematics and we both agree that children shouldn’t be
forced to do mathematics with worksheets. We both believe in teaching students in a
way where they are actively engaged and responsible for their learning. We have
included many games and activities that can be adjusted for all students.
Over the course of ten days, students will learn many things! We will begin by
reviewing numbers and the system by talking about place value, use hands-on and
virtual manipulatives, learn useful strategies for solving problems, play games and
activities to reinforce the important concepts and use money to understand nonproportionate models. Please see the unit chart.
Prerequisites:
Students will need to have been introduced to pre-number concepts in previous
grades such as classifications, patterns, comparisons, conservation, group recognition
and counting strategies.
Rationale:
Making sense of numbers and place value are critical concepts for students to develop
and master because we use it in our everyday lives and it is a major component to our
number system. We deal with place value when we use whole numbers and decimals
and it is necessary for computational algorithms such as addition, subtraction,
multiplication and division.
Unit Standards:
Numbers and Operations
3.1.1.1 Read, write and represent whole numbers up to 100,000. Representations may include
numerals, expressions with operations, words, pictures, number lines, and manipulatives such as
bundles of sticks and base 10 blocks.
3.1.1.2 Use place value to describe whole numbers between 1000 and 100,000 in terms of ten
thousands, thousands, hundreds, tens and ones.
3.1.1.3 Find 10,000 more or 10,000 less than a given five-digit number. Find 1000 more or 1000 less
than a given four- or five-digit. Find 100 more or 100 less than a given four- or five-digit number.
3.1.1.4 Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate
sums and differences. Compare and represent whole numbers up to 100,000 with an emphasis on place
value and equality.
3.1.1.5 Compare and order whole numbers up to 100,000.
3.1.2.1 Add and subtract multi-digit numbers, using efficient and generalizable procedures based on
knowledge of place value, including standard algorithms.
3.1.2.2 Use addition and subtraction to solve real-world and mathematical problems involving whole
numbers. Use various strategies, including the relationship between addition and subtraction, the use
of technology, and the context of the problem to assess the reasonableness of results.
3.1.2.3 Represent multiplication facts by using a variety of approaches, such as repeated addition,
equal-sized groups, arrays, area models, equal jumps on a number line and skip counting.
Add and subtract multi-digit whole numbers; represent multiplication and division in various ways;
solve real world and mathematical problems using arithmetic.
Unit Goals:
This unit is designed for third grade. We hope that in their previous years they will
have learned how to use multiple models to develop an initial understanding of place
value and the base-ten system. By third grade, the students will already know how to
use and represent whole numbers in a variety of ways including composing and
decomposing numbers. Students will also be able to recognize and connect number
words to numerals and the quantities they represent using a variety of models and
representations. We hope that by the end of this unit, students will gain a better
understanding of number sense and the idea of place value to at least 100,000.
Unit Objectives:
Students will be able to understand and represent the place-value structure using the
base ten system.
Students will be able to compare whole numbers and decimals.
Students will be able to recognize and understand proportional and non-proportional
models.
Students will be able to recognize representations for the same number.
Students will be able to compose and decompose numbers.
Developmental Stage:
According to Erik Erickson, socially our students are in the “Industry vs.
Inferiority” stage. At this point in their lives they are starting to recognize their
personal abilities and starting to compare them to others. It is our duty as teachers
to make sure that the children do not feel inferior. We hope to decrease the feeling
of inferiority by have the children work in pairs and in groups to reach common goals.
We also hope to create classrooms where the students feel comfortable asking
questions and sharing their ideas.
According to Jean Piaget, cognitively our students will be at the very beginning
of the concrete operational stage. This is when they are starting to think more
logically about objects and events. They also start to classify objects according to
several features. In our unit, we plan to help expand their cognitive thinking by
giving them tasks where they will need to use logical thinking and do classifications.
Some of these tasks are giving different number representations, comparing and
ordering whole numbers, representing multiplication facts by using a variety of
approaches etc.
Technology:
In all of these unit activities, we will be integrating a variety of technology into
teaching and learning. Besides using slideshows, projectors and the SMARTboard,
calculators will also be available for students to use. These can be useful for playing
place value games, figuring out place values of numbers and help students compute
complex problems.
Educational software such as Everyday Mathematics will be used for practice as
well as grade/level appropriate websites.
Interactive Math Games:
Nat’l Library of Virtual Manipulatives: http://nlvm.usu.edu/en/nav/topic_t_1.html
Adding Math Madness:
(http://www.sheppardsoftware.com/mathgames/Add%20Like%20Mad%20Math/addlike
mad_coin.htm)
Place Value – Matching game: (http://www.quia.com/mc/279741.html)
Shark Numbers: (http://www.ictgames.com/sharkNumbers_v2.html)
Place Value Quiz: (http://www.thatquiz.org/tq/practice.html?placevalue)
Place Value Playoff! Matching standard form with expanded form:
(http://www.quia.com/mc/279741.html)
Virtual Base Ten Blocks: (http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html)
Money – How much change?: (http://www.aplusmath.com/Flashcards/)
Scooter Quest – place value & money:
(http://www.sheppardsoftware.com/mathgames/placevalue/scooterQuest.htm)
Interactive Calculator:
(http://www.bbc.co.uk/schools/ks2bitesize/maths/activities/usingacalculator.shtml)
Text:
Reys, R. E et. al. (2007). Helping Children Learn Mathematics 8th ed. (p. 177-201).
Hoboken, NJ: John Wiley & Sons.
Information for lessons:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L218
http://www.learningandteaching.info/learning/piaget.htm