## The Canoe Project

**Teachers may access additional teacher content relating to this course such as unit guides, standards, and implementation guidelines.**

**Overview**

Students will use their knowledge of mathematical concepts to design a model canoe. Native Hawaiians’ processes of designing, building and navigating a canoe required a deep understanding of mathematical concepts. For example, canoes were carefully engineered to move with the power of the wind and ocean. Polynesians’ precise mathematical intuitions guided their expansion across thousands of miles of open water.

Early settlers of Hawaiʻi used canoes, or waʻa, to make their long voyage. Once they arrived, they used different types and sizes of canoes for fishing, travel along the coast, sport, and war. Regardless of the design, canoe building started with a similar ritual.

The canoe builder (kahuna kālai waʻa) would find a healthy-looking koa tree. He would sleep at a shrine and wait to dream of a special sign that meant the koa tree was healthy. The kahuna kālai waʻa would then go to the tree and look for an ʻelepaio bird. If the bird pecked on the tree, that meant it was no good for canoe building. It the bird avoided the tree, then that signaled it would make a strong canoe.

The kahuna kālai waʻa brought several offerings: a black pig, coconuts, a type of red fish and kava root. He chanted, prayed and presented these things to his gods. The next morning, he would cook the pig in an underground oven (imu) near the tree. Now, he was ready to cut down the tree.

To learn more about canoe building, you can read an excerpt from the “Hawaiian Canoe Building Traditions” by Naomi Chun.

### All of our books are also available in print at Amazon.com

### Curriculum Usage Form

Before downloading the NKH curriculum, please fill out our Curriculum Usage Form/ By providing your teacher information we can continue to reach and improve student’s math experiences in Hawai’i.

**8th Grade Math Standards **

##### Unit 1

**MA.8.NS.1**Understand informally that every number has a decimal expansion; rational numbers have decimal expansions that terminate in zeroes or eventually repeat, and conversely.

**MA.8.NS.2**Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram and estimate the value of expressions (e.g. π2)

**MA.8.EE.1**Know and apply the properties of integer exponents to generate equivalent numerical expressions.

**MA.8.EE.2**

Use square root and cube root symbols to represent solutions to equations of the form x2=p and x3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.

**MA.8.EE.3**

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

**MA.8.EE.4**

Perform operations with numbers expressed in scientific notation, including problems were decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

##### Unit 2

**8.EE.B.5**

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

**8.EE.B.6**

Use similar triangles to explain why the slope *m* is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at *b*.

**8.F.A.1**

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

**8.F.A.2**

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

**8.F.A.3**

Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A=s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

**8.F.B.4**

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

**8.F.B.5**

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

**8.SP.A.1**

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

**8.SP.A.2**

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

**8.SP.A.3**

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

##### Unit 3

**8.EE.C.7**Solve linear equations in one variable.

**8.EE.C.7.a**Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form

*x = a, a = a, or a = b*results (where

*a*and

*b*are different numbers).

**8.EE.C.7.b**Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

**8.EE.C.8**Analyze and solve pairs of simultaneous linear equations.

**8.EE.C.8.a**Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

**8.EE.C.8.b**Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x+2y=5 and 3x+2y=6

3x+2y=6 have no solution because 3x+2y 3x+2y cannot simultaneously be 5 and 6.

**8.EE.C.8.c**Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

##### Unit 4

**8.G.A.1**Verify experimentally the properties of rotations, reflections, and translations.

**8.G.A.1.a**Lines are taken to lines, and line segments to line segments of the same length.

**8.G.A.1.b**Angles are taken to angles of the same measure.

**8.G.A.1.c**Parallel lines are taken to parallel lines.

**8.G.A.2**Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

**8.G.A.3**Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

**8.G.A.4**Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

##### Unit 5

**8.EE.B.6**Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mxy=mx for a line through the origin and the equation y=mx+by=mx+b for a line intercepting the vertical axis at b.

**8.EE.C.7**Solve linear equations in one variable.

**8.EE.C.7.b**Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

**8.G.A.5**Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

**8.G.B.6**Explain a proof of the Pythagorean Theorem and its converse.

**8.G.B.7**Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

**8.G.B.8**Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

**8.G.C.9**Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

##### Unit 6

**8.SP.A.1**Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

**8.SP.A.2**Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

**8.SP.A.3**Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

**8.SP.A.4**Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?