- =20
**All Things Being Equal II**- The equals sign s= ignifies that amounts on each side are the same. The students will use Unif= ix blocks and the corresponding equations to represent equalities between a= dditive amounts. =20
**Comparing Heights I**- Students compare the heights = of two children, measure, compare, and represent one's own height in relati= on to a peer's height, and focus on the differences between heights. =
=20
**Functioning Together**- Students work together to d= evelop multiple representations of a function. The students split up into g= roups of three with each student having a separate responsibility. When all= the input values have been used up, the students are asked to, together, m= ake up a story that describes their function. =20
**Human Graph I**- Students plot themselves on a Cartesian p= lane. Each student will get a large card with a place for an ordered pair: = (x, y), where x refers to hours worked, and y refers to amount earned. The = students must name the coordinate pair for the point they themselves are st= anding on. =20
**Human Graph II**- Students graph the functions k x 2 $/h = and k x 3 $/h. The idea is to show that for each linear function the points= fall onto a straight line. =20
**Number Line - Locations**- Students place themse= lves at points on the number line. Main contexts: stairs, age, money, tempe= rature, and pure number. =20
**Number Line Shortcuts**- The students will use a n= umber line to see how two addends or subtrahends are equivalent to one sing= le change once combined. =20

- =20
**Comparing Strips of Unmeasured Lengths I**- The class is the first of a series that will focus directly up= on the algebraic representation of measurements and their multiplicative re= lations. Children are asked to compare the lengths of strips, to describe t= he relationships between them in multiple ways, and to demonstrate that the= relationships they represent are true. =20
**Comparing Strips of Unmeasured Lengths II<= /a>**- The class is the second of the "Strips of Unmeasured Lengths= " series that will focus directly upon the algebraic representation of meas= urements and their multiplicative relations. Children are asked to compare = the lengths of strips, to use algebraic notation to describe the relationsh= ips between them, and to demonstrate that the relationships they represent = are true. =20
**Comparing Strips of Unmeasured Lengths II= I**- This is the third lesson in the "Strips of Unmeasured Leng= ths" series that focuses directly upon the algebraic representation of meas= urements and their multiplicative relations. We will work with the relation= ship B =3D 3S, focusing on equations and their verbal descriptions and on t= rue and false equations and statements. =20
**Multiplicative Candy Boxes I**- This class = centers on the possible amounts of candies two children, Juan and Marcia, h= ave. Juan has a box of candy and Marcia has twice as much candy. What are t= he possible amounts of candies they might have? =20

- =20
**Enacting and Solving Equations**- Student= s enact and discuss a situation where two children have amounts of candies.= Some of the candies are visible, others are inside opaque tubes or boxes. = After considering multiple possibilities they are told that the children ha= ve the same amount of candies. The situation corresponds to the equation 3x= + y + 6 =3D x + y + 20, where x is the amount of candies per tube and y is= the amount of candies per box. Students will be asked to discuss and to re= present the situation, to solve the equation that corresponds to the situat= ion, and to solve other written equations with similar structure. =20

- =20
**Box Extremum**- Students will start by finding average rate= s of change for a non-linear function over increments of the independent va= riable. The size of the increments will decrease to introduce the idea of u= sing tangent lines to find instantaneous rates of change of linear and non-= linear functions. Students will see what a tangent looks like at the extrem= a of a graph. Students will then create a box that maximizes the volume and= see how determining the extrema of a graph can help to find the maximum vo= lume. =20
**Candy Experiment**- Students will create their own data= to construct a graph and equation of negative and fractional slope. =
=20
**Can We Predict Differences?**- Students will predict, produce,= and compare linear and non-linear function graphs used to represent the nu= mber of punches on a balloon. =20