Use concepts and properties of equivalence and relational thinking to represent and compare numerical expressions, algebraic expressions or equations.
Anchor Standard 4 emphasizes the representation of expressions and equations.
Students will represent addition, subtraction, multiplication, division expressions and equations using a variety of models. They will decompose and compose fractions to add, subtract, and compare.
Finally, students will create and analyze true/false equations and expressions.
Determine if numerical equations and numerical expressions of whole numbers and decimals to hundredths, using place value, properties of mathematics and the four operations, are true or false and find the missing value in an open number sentences without carrying out the calculation.
Represent multiplication up to two-digit by two-digit expressions and equations in a variety of ways, using place value, the properties of algebra and the four operations.
Represent division expressions and equations of multi-digit whole numbers by one-digit divisor in a variety of ways, using place value, the properties of algebra and the four operations.
Decompose and compose fractions to add and subtract fractions with like denominators and fractions greater than one with numerical expressions and numerical equations. Use these expressions and equations to compare fractions that are halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths.
Represent problems as numerical expressions and numerical equations requiring addition, subtraction and multiplication of multi-digit whole numbers using properties of mathematics and the relationship between addition/subtraction and multiplication/division.
Write true/false numerical equations and numerical equivalent expressions in a variety of ways, using all four operations, to expand and simplify problems.
Make conjectures and justifications about properties of operations, using the properties of algebra.
This activity is so simple, but so much fun! Go outside in the winter and write equations (or expressions) in the snow. Students may wish to use their gloved fingers or a stick or pencil. Practice the commutative, associative, and distributive properties of addition and multiplication. Decompose and recompose fractions. Students could also use snow writing to practice standard multiplication and division algorithms.
This activity could be modified for summer weather using sidewalk chalk.
Possible Extension: Use this activity as a carousel or "scoot" activity: students will first write expressions, then move from expression to expression and solve each on a piece of paper.
Send students outside to collect as many natural items (sticks, leaves, acorns, rocks, etc.) as they can find in a set amount of time. Then, direct them to sort their items into categories (big leaves, little leaves, rocks... / birch, maple, oak, fir... /red leaves, orange leaves, yellow leaves...).
Find the fractional amount of each category (⅓ of the leaves are big, ⅔ of the leaves are little). Students could also write equations to represent their findings: three groups of 10 leaves equal 30 leaves, ⅓ big leaves and ⅔ little leaves equal 1 group of leaves.
Possible Extension: Extend this activity to a broader space: how many trees are in your outdoor area? How many of those trees are birch? How many are ash? Maple? Print some simple tree id photos or use kid-friendly field guides to help students identify species. Practice writing equivalent fractions with this information.
Using sidewalk chalk, sticks, or rope, split your outdoor workspace into a variety of fractions. Start easy, with half, thirds, and fourths; then get more complex, with 7ths, 12ths, etc. Sketch your work in a notebook to add a second visual representation.
Discuss the relationship between each fraction set: which denominators have the smallest sections? Which denominators were easiest to create? Which were the most complicated?
Possible Extension: Measure the area of your outdoor space before splitting it into fractions. Find the area of each fraction set, and write equations! If the entire area is 20 square feet, then what is the area of each 4th?