### Math Continuum Quarter 1

K.NS.1: Count to at least 100 by ones and tens and count on by one from any number

Count Around is an activity that can be used to help students with counting and counting on. Have the students sit in a circle. Then, toss a soft ball to one of the students and have them pick a number from 0-20. Next, that student tosses the ball to a different student and the student that catches the ball says the number that comes next. Continue play until everyone has had a chance to catch the ball at least once. Encourage students to think of the number that comes next even if they are not the ones to catching the ball. [There are variations to this activity, such as, starting from 0, count by tens with each toss of the ball.]

K.NS.2b Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

Practice Activity: Have students pick nine numbers from 0-10 and place them on a Bingo card like below. Then, show students a number word, such as “five”, and have them mark that on their Bingo card if they used the number 5. Continue play until someone wins. [A variation of this is to have students pick nine numbers from 0-20 and place them on their Bingo card. Then, show students a picture of a number of objects and have them mark that number on their card if they used that number.]

K.DA.1: Identify, sort, and classify objects by size, number, and other attributes. Identify objects that do not belong to a particular group and explain the reasoning used.

Provide a bag with different objects for each student or groups of students. For example, a bag might have 4 red counters, 6 blue counters, and 7 yellow counters. Have the students sort the objects by color. Then, have them arrange them in order from least to most (i.e. red, then blue, then yellow).

PTS K. CC.3: Recognize 0-10 out of order

PTS G.1a: Identify 2-D shapes: circle, square, rectangle, oval, diamond, triangle.

1.NS.1: Count to at least 120 by ones, fives, and tens from any given number. In this range, read and write numerals and represent a number of objects with a written numeral.

a) Count to 120 by ones, fives, and tens. b) Count to 120 by ones, fives, and tens beginning at 40. c) Read the following numbers: 43, 116, 79

1.NS.2: Understand that 10 can be thought of as a group of ten ones — called a “ten." Understand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Understand that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

a) What number does the model below show? b) Draw a picture like the one above to show the number 17. c) Draw a picture like the one above to show the number 60.

1.M.3: Find the value of a collection of pennies, nickels, and dimes.

2.NS.2: Read and write whole numbers up to 1,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000.

a) Write 365 using words and expanded form.

2.CA.7: Create, extend, and give an appropriate rule for number patterns using addition and subtraction within 1000.

a) What are the next two numbers in the pattern below?

Describe the rule for this pattern.

110, 210, 310, ____, ____

b) What are the next two numbers in the pattern below?

Describe the rule for this pattern.

500, 490, 480, ____, ____

c) Activity: Have students create their own number pattern. Then, have them switch patterns with another student and try to determine each.

3.C.1: Add and subtract whole numbers fluently within 1000.

Evaluate each expression.

345 + 89 86 − 45 502 + 293

784 − 691 02 − 165 487 + 465

3.DA.1: Create scaled picture graphs, scaled bar graphs, and frequency tables to represent a data set—including data collected through observations, surveys, and experiments—with several categories. Solve one- and two-step “how many more” and “how many less” problems regarding the data and make predictions based on the data.

Activity: Students can conduct an observation, survey, or experiment. They can collect, organize, and display their data, and make observations based on their data display. (Examples: conduct a survey about favorite food, color, etc.; observe and tally the different colors of shirts classmates wear to school on a given day.)

4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

a) Milagro has 52,500 baseball cards. Julie has 109,078 baseball cards. Carl has 1,048 baseball cards.

How many more cards does Julie have than Milagro and Carl combined?

b) Barry and Tina participated in a reading contest last year. They read a combined total of 12,082 pages. Barry read 5,916 pages. How many pages did Tina read?

No Unit Assessments

6.NS.1: Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.

A submarine was situated 400 feet below sea level. If it ascends 250 feet, what is its new position? Represent this situation on a number line. What does 0 represent in this situation?

6.NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts.

a) Plot the following numbers on a number line. −3.6, 1.5, −1 1 4 , 5 3

b) In town A, the temperature is −4℃. In town B, the temperature is −5℃.

Write an inequality statement that compares the temperatures in the two towns and describe the meaning of the statement in terms of the context.

6.AF.8: Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Vicky created a map of her neighborhood on a coordinate plane. Her house is located at (-3.5, 6) and her school is located at (-3.5, -1). How far, in units, is Vicky’s house from her school?

7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations, such as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error.

Last year, Kim earned $8 per hour at her job. This year, Kim earns $10 per hour at her job. What is the percent of increase, in dollars earned per hour, from last year to this year?

7.C.8: Solve real-world problems with rational numbers by using one or two operations

a) The temperature in town A is -3.5 degrees Celsius. The temperature in town B is 2.5 times colder. What is the temperature in town B?

b) Larry bought 3 pounds of apples and one bag of oranges at the store. The apples cost $1.75 per pound and the bag of oranges cost $2.99. What was the total cost of Larry’s purchase? Do not include tax.

AI.L.1: Understand that the steps taken when solving linear equations create new equations that have the same solution as the original. Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients. Explain and justify each step in solving an equation, starting from the assumption that the original equation has a solution. Justify the choice of a solution method.

Solve the equation and inequality.

a) 1/5 (𝑝 − 14) = 10 + 𝑝

b) 2.5𝑚 − 7(𝑚 − 3) ≥ 40

AI.L.2: Represent real-world problems using linear equations and inequalities in one variable and solve such problems. Interpret the solution and determine whether it is reasonable

Jenny starts a scarf knitting business. She spends $160 on supplies to start the business, and she spends $4.50 to make each scarf. She sells each scarf for $12. Write an inequality that can be used to determine the number of scarves Jenny must sell in order to make a profit. What is the minimum number of scarves Jenny must sell in order to make a profit?

AI.L.3: Represent real-world and other mathematical problems using an algebraic proportion that leads to a linear equation and solve such problems.

a) If 3 lbs. of potato salad serves 10 people, write an equation that can be used to determine the amount of potato salad needed to serve 52 people. How much potato salad is needed to serve 52 people?

b) Solve: (3𝑦−8)/12 = 𝑦/5

AI.F.2: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Identify independent and dependent variables and make predictions about the relationship

Joe ran from his home to school at a constant speed. He took a short break and then ran back home, but at a slower non-constant speed. Joe ran along a straight path to and from school. Sketch a graph to represent Joe’s distance from his home over time. Identify the independent and dependent variables.

AI.L.5: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts.

A fishing lake was stocked with 300 bass. Each year, the population of bass decreases by 25. Write an equation that can be used to determine the number of bass in the lake after a given number of years since being stocked. Be sure to define your variables. Graph your equation and determine what the intercepts and slope represent in this problem.

AII.DSP.2: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient.

AII.SE.2: Solve systems of two or three linear equations in two or three variables algebraically and using technology

Solve the following system of equations:

𝑥 + 𝑦 + 𝑧 = 12

6𝑥 − 2𝑦 − 𝑧 = 16

3𝑥 + 4𝑦 + 2𝑧 = 28