SELECTED TERMS AND SYMBOLS The following and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them. The below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers. Algorithm Dividend Divisor Exponents Expression Measurement Division (or repeated subtraction) Multiplicand Multiplier Partition Division (or fair-sharing) Product Properties Quotient Remainder STRATEGIES FOR TEACHING AND LEARNING Students should be given ample opportunities to explore numerical expressions with mixed operations. This is the foundation for evaluating numerical and algebraic expressions that will include whole-number exponents in Grade 6. There are conventions (rules) determined by mathematicians that must be learned with no conceptual basis. For example, multiplication and division are always done before addition and subtraction. Begin with expressions that have two operations without any grouping symbols (multiplication or division combined with addition or subtraction) before introducing expressions with multiple operations. Using the same digits, with the operations in a different order, have students evaluate the expressions and discuss why the value of the expression is different. For example, have students evaluate 5 × 3 + 6 and 5 + 3 × 6. Discuss the rules that must be followed. Have students insert parentheses around the multiplication or division part in an expression. A discussion should focus on the similarities and differences in the problems and the results. This leads to students being able to solve problem situations which require that they know the order in which operations should take place. After students have evaluated expressions without grouping symbols, present problems with one grouping symbol, beginning with parentheses, then, in combination with brackets and/or braces. Have students write numerical expressions in words without calculating the value. This is the foundation for writing algebraic expressions. Then, have students write numerical expressions from phrases without calculating them.
Money for Chores Constructing Task Individual/Partner Task Write and evaluating expressions. Hogwarts Cup Constructing Tasks Individual/Partner Task Evaluate expressions with parentheses ( ), brackets [ ] and braces { }. Hogwarts House Cup Part 2 Practice Task Individual/Partner Task Evaluate expressions with parentheses ( ), brackets [ ] and braces { }. Patterns R Us Constructing Task Partner/Small Group Task Exploring powers of ten with exponents Multiplication in a Row Practice Task Small Group/Partner Task Multiply multi-digit numbers The Grass is Always Greener Constructing Task Small Group/ Individual Task Applying multiplication to problem solving situations Division Four in a Row Practice Task Partner/Small Group Task Divide four-digit dividends by one and two-digit divisors Are All Constructing Task Individual/Partner Task Conceptual Understanding of Division Problem Types Start of the Year Celebration Performance Task Individual Task expressions which involve multiplication and division of whole numbers As this unit has no Culminating Task, you may pair/modify to include all unit standards in combination. Scaffolding Task: Order of Operations STANDARDS FOR MATHEMATICAL CONTENT CCGPS.5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5 + 7 – 8 18 – 9 + 6 16 ÷ 4 + 10 6 + 6 – 3 ( 13 – 3) x 6 Teacher Bingo sheet Cut into strips for Game The sum of two and multiplied by four The quotient of eight and two added to six The sum of six and two multiplied by twelve The sum of sixteen and two subtracted by ten The product of and two added to six The sum of six and seven subtracted by twelve The product of six and one subtracted by eight The sum of twenty two and six subtracted by eight The quotient of twelve and two added to seven The sum of nine and five subtracted by the product of four and three The quotient of sixteen and two added to six The product of eight and two subtracted by ten The sum of two and two multiplied by six The product of seven and seven added to six The product of two and two subtracted from fourteen
Does anyone have the same answer but a different way to explain it? Do you understand what _______ is saying? Can you convince the rest of us that your answer makes sense? can you explain to us what _____ is doing? DIFFERENTIATION Extension the player to decide what number to use for the input number. Encourage students to use mental math and estimation to determine the output number. Ask students to devise their own rules. Intervention Provide a student recording sheet where the Input values are filled in 0-10. Use this task in direct, small group instruction. Ask students to devise their own rules. TECHNOLOGY CONNECTION Students can enter a value, find the output value, or determine the rule. Students an input value and are given the output value. They then need to determine the rule. Students choose the level of difficulty before beginning the game.
Did you find all of the possible ways that Manuel could have painted windows and doors? How do you know? Constructing Task: Hogwarts Cup STANDARDS FOR MATHEMATICAL CONTENT MCC5.OA.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. STANDARDS FOR MATHEMATICAL PRACTICE 1. Make of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE