3: Building Number Sense- Understanding Whole Number Operations and Their Properties
- Page ID
- 181690
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Numbers are everywhere! From counting seats on a bus to sharing churros at a snack stand (Morgan and Grandpa, see story below :) ), whole number operations—addition, subtraction, multiplication, and division—help us make sense of the world around us. In this chapter, we will explore these essential operations using models and strategies that highlight their fundamental properties. We will see how numbers relate through commutativity, associativity, and distributive properties, and how inequalities and exponents fit into the bigger picture of mathematical thinking. By understanding these concepts deeply, we can develop strong mental computation skills that will serve us in various real-life situations.
As future elementary teachers, mastering whole number operations is more than just learning procedures—it’s about fostering number sense in young learners. Through this chapter, we will uncover how whole number properties help solve everyday problems and why they are crucial for effective math instruction.
Chapter Learning Objectives
- SLO 3.1 Students will demonstrate a comprehensive understanding of whole number operations, including addition, subtraction, multiplication, and division, by modeling each operation with set and measurement models and analyzing their properties.
- SLO 3.2 Students will apply strategies for mental computation in addition, subtraction, and multiplication across different bases and demonstrate mastery of basic facts using commutativity, associativity, and distributive properties.
- SLO 3.3 Students will analyze and apply the properties of whole numbers in relation to inequality, including transitivity, addition, and multiplication properties of "less than," as well as use addition to establish comparative relationships.
- SLO 3.4 Students will demonstrate an understanding of whole number exponents by defining exponents through repeated multiplication and proving fundamental exponent rules.
- SLO 3.5 Students will evaluate numerical expressions involving whole numbers using the conventional order of operations (including parentheses, exponents, multiplication, division, addition, and subtraction), to arrive at a unique and correct solution.
Essential Questions
- How do the properties and operations of whole numbers help us make sense of and solve real-world problems?
- How can understanding whole number concepts and strategies support effective math instruction for young learners?
Learning That Transfers
Students will analyze and apply whole number operations—addition, subtraction, multiplication, and division—to real-world contexts by developing mathematical models that demonstrate problem-solving strategies for everyday situations and elementary-level teaching. They will evaluate and adapt these models to support young learners’ conceptual understanding and problem-solving skills.
Number Sense Groove
NEED AUDIO FOR STORY
Morgan and Grandpa’s Mathematical Adventure
One bright morning, as Morgan arose, Grandpa said, “Let’s go where the number wind blows! Numbers are grand, they’re everywhere seen, Let’s find their magic in places between!”
They hopped on a bus—oh what a delight! Numbers on seats, left and right. “See here, my dear,” Grandpa said with a grin, “Addition is easy, let’s begin!”
Morgan looked, eyes open wide, “Two kids sit here, and three more beside. If we add them together, it’s easy to do, Two plus three, why look, it’s just five—woohoo!”
Down at the park, the swings went high, Morgan saw seagulls swoop through the sky. “Grandpa, if eight birds fly off in a dash, And three fly back, what’s left in a flash?”
Grandpa chuckled, “That’s subtraction, my dear! Take eight, remove three, and five remain here!” Morgan beamed, “Oh, it’s quite clear! Numbers are fun, let’s find more near!”
They stopped for a snack at a sweet little stand, Grandpa held three churros in his hand. “If each one holds two bites just right, How many bites will we have in sight?”
Morgan thought, “Three times two, Means six sweet bites—one for me, one for you!” Grandpa clapped, “That’s multiplication, you see, Numbers at work, so brilliantly!”
Then at the pond, a puzzle was found, Ten ducks lined up, splashing around. “They split into groups, two per a row, How many rows do they make in a show?”
Morgan counted, “One, two, three, four, five, Dividing by two keeps math alive! Ten ducks split makes five neat lines, Division, Grandpa, is full of designs!”
The sun dipped low, the sky turned gold, Morgan felt proud, so brave and bold. “Numbers are everywhere, big and small, And now I see, I can use them all!”