more disconnected thoughts from the MSIS at the Shanghai American School
Opening: Formative Assessment is challenging to implement because it necessitates us to adjust our teaching. It’s so much easier to believe that students walked out of the door understanding what happened than to find out that they didn’t and need to adjust.
Why MSIS – to help shift mathematical practices in schools. How do we return and improve mathematical instruction at our schools?
Start with the Problem! How else will students begin to realize what they know, what methods are efficient / inefficient, and how these problems relate.
Algebra – create the expressions from scenarios. Relate independent and dependent variables. How can a simple scenario be reworked to focus sometimes on the dependent and other times on the independent?
Visualpatterns.org – keep using them!
MS Progression of EE
6.EE.1 Write and evaluate numerical expressions involving whole number exponents
6.EE.2 Write, read and evaluate expressions in which letters stand for numbers.
6.EE.3 Write expressions that record operations with numbers and with letters standing for numbers (i.e. Express the calc. “Subtract y from 5 as 5-y”)
3a – Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity (i.e. 2(8 + 7) as a product of two factors; (8 + 7) as a single entity and a sum of tw terms.
3b – Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order t when there are no parentheses to specify a particular order (Order of Operations)
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related (i.e. a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05”
3c – Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2+x) to produce 6 + 3x;
apply the distributive property to the expression 24x + 18y to produce 6(4x + 3y);
apply properties of operations to y + y + y to produce the equivalent expression 3y
7.EE.1 Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients.
6.EE.4 Identify when two expressions are equivalent.
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q (nonnegative rational numbers)
7.EE.3 Solve multi-step real life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions and decimals)
Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies (i.e. If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary, or $2.50 for a new salary of $27.50)
6.EE.8 Write an inequality of the form x>c or x<c to represent a constraint or condition in a problem. Recognize that inequalities of the form x>c or x<c have infinitely many solutions; represent solutions of such inequalities on number line diagrams
6.EE.9 Use variables to represent two quantities in a problem that change in relationship to one another; write an equation to express one quantity (dependent variable in terms of independent variable)
Analyze the relationship between the dep. and ind. variables using graphs and tables and relate these to equation. (example – in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d=65t to represent the relationship between distance and time.)
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities
a) Solve word problems leading to the equations of the form px + q = r and p(x+q)=r where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used. (ex. the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?)
b) Solve word problems leading to inequalities of the form px + q > r or px + q <r. Graph the solution set of the inequality and interpret it in the context of the problem. (ex As a salesperson, you are paid $50 / week plus $3 per sale. This week you want your paty to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.
Grade 6: x + 6 = 12 or 6x=12
Grade 7: 4(x+6) = 12
Grade 8: 9 – 4(x+6) = 12 + x