The situation in the problem involves trying to figure out how many pennies in a 50-penny roll were minted before 1983 and how many were minted after, using only the weight of the roll to make your determination. The necessary background, provided in the problem, is that pennies before 1983 are heavier (3.11 grams) than pennies that were minted after 1983 (2.5 grams).

One of the things I like about the problem is that it can be solved using different problem -solving strategies: making tables, guess and check, or an algebraic approach.

The first page of the link above is the student handout. The second page is for teachers and includes support questions (to help struggling students) and push questions (to engage finished student in further exploration). The push and support questions Patricia has written are a great way to keep all the students in a mixed-level math class productively engaged with the same problem.<<Read here for more information on how to use push and support questions.>>

This problem can be used to explore the the following TASC standard:

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

This problem is also a good way to reinforce the concepts of rate of change and starting amount which are raised in Unit 3 of the CUNY HSE Curriculum Framework.

Here’s the original problem that Patricia adapted for use in the adult numeracy and HSE classroom. It comes from the Illustrative Mathematics website.

]]>The situation in the problem involves someone who needs to hire a mechanic to fix their furnace. There are three different companies to choose from, each with their own function for calculating labor costs. Students have to choose the best company and to defend their choice.

One of the things I like about the problem is that it can be solved using tables, graphs, or an algebraic approach. I also like that it requires students to use math to make an mathematical argument about which company is the best choice.

In addition to the student handout, the link above also includes support questions (to help struggling students) and push questions (to engage finished student in further exploration). The push and support questions Patricia has written are a great way to keep all the students in a mixed-level math class productively engaged with the same problem.<<Read here for more information on how to use push and support questions.>>

This problem can be used to explore the the following TASC standard:

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

This problem is also a good way to reinforce the concepts of rate of change and starting amount which are raised in Unit 3 of the CUNY HSE Curriculum Framework.

Here’s the original problem that Patricia adapted for use in the adult numeracy and HSE classroom. It comes from the Illustrative Mathematics website.

]]>This is a good activity for teachers who are using (or reviewing) Unit 1 of the CUNY HSE Math Curriculum Framework and want to give students some practice with the TI-30XS calculator.

In Unit 1 of the CUNY HSE Math Curriculum Framework there is an activity called “My Teacher is a Computer” and another called “The Function Game”.

- “My Teacher is a Computer” comes in the beginning of the lesson, where the teacher has a function rule in their head. Students take turns giving numbers to input into the teachers function and the teacher tells students what number comes out with each input. Students keep track of the inputs and outputs and use the growing table to try and guess the function rule.
- “The Function Game” comes at the end of the lesson (there are two other activities between “My Teacher is a…” and “The Function Game”). In this activity students come up with a function and then use that function to fill out some input/outputs a table. Then they give the table to another student, who then has to figure out the function rule.

The TASC calculator – the TI-30XS has a feature that allows students to enter a function into the calculator. They they can set the calculator to take inputs from another student and give the output. The other student can keep putting in numbers until they are able to guess the function. It is a kind of a combination of the two activities above.

Here’s a brief video to show you how it can be done:

You can also enter a function into the calculator and get a completed input/output table. It is a very similar set-up as using the calculator to play the function game, except for one step, which is described in the step-by-step instructions. Basically, when you get to the menu of three options, instead of choosing “Ask-x” you choose “Auto”.

I’m curious as to how teachers might use this feature of the calculator with students, so please share any ideas you have in the comment section below.

- What are some benefits to showing students how to enter a function equation and get a completed table of input and output values?
- What might be some interesting function equations students could enter and then do a notice/wonder with the completed function table?

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The focus words for this unit are: cell, divide, multiply, fungus, individual, reproduction, separate, exponential, microscopic, nucleus, nutrient, fuel, process, and matter

]]>The focus words for this unit are: specimen, structure, function, organic, membrane, fuel, osmosis, cycle, producer, and consumer

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The following pages describe the Physical Sciences standards assessed on the TASC and provide sample items for each standard. The goal of this document is to describe the ideas that students need to understand so that teachers understand what they need to teach. The sample items (practice questions) in this document **can** be used with students since have already been released to the public. Also noted is whether each standard is a high, medium or low emphasis topic on the TASC.

The standards, content descriptions and sample items are based on the DRC/CTB TASC Item Specifications and the TASC Test Science Practice Items. In addition, we used the Next Generation Science Standards (NGSS) and A Framework for K-12 Science Education for reference, since the TASC standards are based on NGSS standards with the same title.

Here are a few sample questions from the document linked above:

The linked Google document will allow comments. Please let us know if you have questions, comments or suggestions.

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The following pages describe the Life Sciences standards assessed on the TASC and provide sample items for each standard. The goal of this document is to describe the ideas that students need to understand so that teachers understand what they need to teach. The sample items in this document can be used with students since have already been released to the public. Also noted is whether each standard is a high, medium or low emphasis topic on the TASC.

The standards, content descriptions and sample items are based on the DRC/CTB TASC Item Specifications and the TASC Test Science Practice Items. In addition, we used the Next Generation Science Standards (NGSS) and A Framework for K-12 Science Education for reference, since the TASC standards are based on NGSS standards with the same title.

Here are a couple of the sample questions in the document linked above:

Which sequence represents the levels of biological organization from smallest to largest?

(1) organism → cell → tissue → organelle → organ system → organ

(2) organ system → organ → organism → cell → tissue → organelle

(3) organelle → organ system → cell → organism → tissue → organ

(4) organelle → cell → tissue → organ → organ system → organism

Which process uses energy to combine inorganic molecules to synthesize organic molecules?

(1) respiration

(2) digestion

(3) photosynthesis

(4) decomposition