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New York - Mathematics: Middle School
New York City: Performance Standards | Adopted:
1.1.1: M1. Number and Operation Concepts
1.1.1.1: M1a. Consistently and accurately add, subtract, multiply, and divide rational numbers.
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
Sums and Differences with Decimals
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line. 5 Minute Preview
Multiplying with Decimals
Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview
Estimating Sums and Differences
Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences. 5 Minute Preview
Fractions with Unlike Denominators
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview
Multiplying Fractions
Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview
Dividing Fractions
Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview
Multiplying Mixed Numbers
Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
Dividing Mixed Numbers
Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
1.1.1.1: M1b. Use and understand the inverse relationships between multiplication and division, and exponentiation and root-extraction.
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
1.1.1.1: M1c. Apply and convert the different kinds and forms of rational numbers.
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
1.1.1.1: M1d. Be familiar with characteristics of numbers.
Finding Factors with Area Models
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview
1.1.1.1: M1e. Interpret percent as part of 100.
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
1.1.1.1: M1f. Describe and compare quantities by using whole numbers up to 10,000.
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
1.1.1.1: M1g. Order numbers with the > and
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
Ordering Percents, Fractions, and Decimals Greater Than 1
Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview
1.1.1: M2. Geometry and Measurement Concepts
1.1.1.1: M2a. Be familiar with assorted two- and three-dimensional objects.
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
1.1.1.1: M2b. Identify similar and congruent shapes and use transformations in the coordinate plane.
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
1.1.1.1: M2c. Identify three dimensional shapes from two dimensional perspectives; draw two dimensional sketches of three dimensional objects.
3D and Orthographic Views
Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview
1.1.1.1: M2d. Determine and understand length, area, and volume.
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
1.1.1.1: M2e. Recognize similarity and rotational and bilateral symmetry in two- and three-dimensional figures.
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
1.1.1.1: M2f. Analyze and generalize geometric patterns.
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
1.1.1.1: M2g. Measure angles, weights, capacities, times, and temperatures using appropriate units.
Elapsed Time
Calculate the difference between the times given by two analog clocks. Rotate the hands of the clocks to change the time and see how the calculation changes. 5 Minute Preview
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
Triple Beam Balance
Learn how to determine the mass of an object using a triple beam balance. The mass of a variety of objects can be determined using this simulated version of a common real-world laboratory tool for measurement. 5 Minute Preview
1.1.1.1: M2i. Reason proportionally in situations with similar figures.
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
1.1.1.1: M2j. Reason proportionally with measurements.
Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
1.1.1: M3. Function and Algebra Concepts
1.1.1.1: M3a. Discover, describe, and generalize patterns, and represent them with variables and expressions.
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
1.1.1.1: M3b. Represent relationships.
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
1.1.1.1: M3c. Analyze tables to determine functional relationships.
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Quadratics in Polynomial Form
Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview
Exponential Functions
Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview
Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
1.1.1.1: M3d. Find solutions for unknown quantities in linear equations.
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
1.1.1: M4. Statistics and Probability Concepts
1.1.1.1: M4a. Organize and display data.
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview
1.1.1.1: M4b. Analyze data with respect to frequency and distribution.
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
1.1.1.1: M4c. Analyze central tendencies of data.
Describing Data Using Statistics
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview
1.1.1.1: M4d. Make conclusions and recommendations based on data analysis.
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
1.1.1.1: M4h. Represent and determine probability, recognize equally likely outcomes, and construct sample spaces.
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
1.1.1.1: M4i. Make predictions based on experimental or theoretical probabilities.
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
1.1.1.1: M4j. Predict the result of a series of trials once the probability for one trial is known.
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
Correlation last revised: 9/5/2008
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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