{"id":3573,"date":"2025-09-01T01:00:00","date_gmt":"2025-09-01T01:00:00","guid":{"rendered":"https:\/\/www.terc.edu\/adultnumeracycenter\/?p=3573"},"modified":"2025-08-29T18:32:45","modified_gmt":"2025-08-29T18:32:45","slug":"will-this-be-on-the-test-september-2025","status":"publish","type":"post","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/will-this-be-on-the-test-september-2025\/","title":{"rendered":"Will This Be on the Test? (September 2025)"},"content":{"rendered":"\n

by Aren Lew<\/p>\n\n\n\n

\n\n\n\n

Welcome to the latest installment of our series, \u201cWill This Be on the Test?\u201d Each WTBotT features a new question similar to something adult learners might see on a high school equivalency test and a discussion of how one might go about tackling the problem conceptually.<\/em><\/em><\/p>\n\n\n\n

\n\n\n\n

Welcome back to our continuing exploration of how to bring real conceptual reasoning to questions students might encounter on a standardized test. <\/p>\n\n\n\n

Here\u2019s a question inspired by a situation I encountered this summer. Where do you<\/em> see math in your life that might lend itself to interesting explorations? See Building Classroom Community in an Online Environment<\/a> by Jean Oviatt-Rothman for more ideas about how real world math can come into the classroom.<\/p>\n\n\n\n

Here is this month\u2019s question:<\/a><\/p>\n\n\n

\n
\"Question:<\/figure>\n<\/div>\n\n\n
\"\"<\/figure>
\n

How can you approach this question in a way that makes sense to you<\/em>? What conceptual understandings or visual tools can you bring to bear? What mathematical concepts do students really<\/em> need to be able to tackle this problem? <\/strong>How might your real-world experience help you reason about this?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

<\/div>\n\n\n\n

Here are some approaches:<\/p>\n\n\n\n

1. Draw a picture. <\/strong>The numbers in this question aren\u2019t that big, so it doesn\u2019t take long to sketch out the whole group. A student might draw a picture something like this, drawing out the swimmers and assigning lifeguards to each group of six swimmers:<\/p>\n\n\n

\n
\"20<\/figure>\n<\/div>\n\n\n

How might this picture help a student answer the question? What ideas do you have about the swimmers who aren\u2019t in a group of six?<\/p>\n\n\n\n

2. Make a table. <\/strong>A slightly more abstract way of making sense of the relationships in this scenario is to make a table showing how many swimmers can be protected by a certain number of lifeguards. Each lifeguard can protect 6 swimmers, so a table could look like this:<\/p>\n\n\n\n

Lifeguards<\/th>Swimmers<\/th><\/tr><\/thead>
1<\/td>6<\/td><\/tr>
2<\/td>12<\/td><\/tr>
3<\/td>18<\/td><\/tr>
4<\/td>24<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The number 20 doesn\u2019t show up in the \u201cswimmers\u201d column, so how does the table help us answer the question? We can see that 3 lifeguards will only protect 18 swimmers, so that is not enough. What does that mean about the number of lifeguards required? What do we do with the information that 4 lifeguards can protect 24 swimmers when we only need to protect 20?<\/p>\n\n\n\n

3. Check the answer choices<\/strong>. An often reliable strategy for approaching a multiple choice question is to consider each answer choice as a separate yes\/no question. This can be inefficient, but in this case, it could be a good way in. Because we are looking for the smallest number of lifeguards needed, a student can start with the smallest number and work their way up until they get to a number of lifeguards that is enough. It could look like this:<\/p>\n\n\n\n

\n
\n

<\/p>\n<\/div>\n\n\n\n

\n

Answer choice A: Is 3 lifeguards enough to protect 20 swimmers? <\/strong><\/em><\/h3>\n\n\n\n

No, because 3 lifeguards can only protect 18 swimmers.<\/em><\/p>\n\n\n\n

Answer choice B: Is 4 lifeguards enough to protect 20 swimmers? <\/strong><\/em><\/h4>\n\n\n\n

4 lifeguards could protect 24 swimmers, so that is enough to protect 20 swimmers.<\/em><\/p>\n\n\n\n

Answer choices C, D, and E: <\/strong><\/em><\/h4>\n\n\n\n

I don\u2019t need to check any further answer choices because 4 is enough and the other numbers are bigger than 4.<\/em><\/p>\n<\/div>\n\n\n\n

<\/div>\n<\/div>\n\n\n\n

In the College and Career Readiness Standards for Adult Education<\/a>, this question falls under standard 6.RP.3: \u201cUse ratio and rate reasoning to solve real-world and mathematical problems\u2026\u201d When we think about questions involving ratios, many of us turn to the cross product. This may feel like the kind of question where setting up and solving a proportion is a quick and efficient way to the answer. In this case, using the cross product will give an answer that 3.333\u2026 lifeguards are needed. Not only is this answer not among the answer choices, but it doesn\u2019t make sense because you can\u2019t have a fraction of a lifeguard. I have seen many students pick the answer choice that is closest to their answer when their calculation gives an answer that is not among the answer choices. In this case, that would lead to picking B, an incorrect answer, even though this is<\/em> a situation involving proportional reasoning and even though 3.333\u2026 is<\/em> a correct answer to a proportion that models the situation.<\/p>\n\n\n\n

Questions like this remind us of the importance of Standard for Mathematical Practice 2 (MP.2)<\/a>: \u201cReason abstractly and quantitatively.\u201d It states that, \u201cMathematically proficient students bring two complementary abilities to bear on problems involving quantitative relationships: The ability to decontextualize<\/em> \u2026 and the ability to contextualize<\/em>\u2026.\u201d This means that it is important to be able to work abstractly with quantities, for example to set up proportions using the numbers from a scenario, but it is equally important to keep checking in with the context.<\/p>\n\n\n\n

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\"\"<\/figure>
\n

Aren Lew has worked in the field of adult numeracy for over ten years, both as a classroom teacher and providing professional development for math and numeracy teachers. They are a consultant for the SABES Mathematics and Adult Numeracy Curriculum & Instruction PD Team<\/a> at TERC<\/a><\/em> where they develop and facilitate trainings and workshops and coach numeracy teachers. They are the treasurer for the Adult Numeracy Network<\/a><\/em>.<\/p>\n<\/div><\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

by Aren Lew<\/p>\n

<\/em>Welcome to the latest installment of our series, \u201cWill This Be on the Test?\u201d Each WTBotT features a new question similar to something adult learners might see on a high school equivalency test and a discussion of how one might go about tackling the problem conceptually.<\/em><\/p>\n

Welcome back to our continuing exploration of how to bring real conceptual reasoning to questions students might encounter on a standardized test. <\/p>\n

Here\u2019s a question inspired by a situation I encountered this summer.  » Read more<\/a><\/p>\n","protected":false},"author":16,"featured_media":1149,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"on","_relevanssi_pin_for_all":"on","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"1602,1729,1138,2924,2231,2021","_relevanssi_noindex_reason":"","footnotes":""},"categories":[11,15,16,106,134,107,19,20],"tags":[121,49,58,135,155,97],"class_list":["post-3573","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-estimation","category-hiset-and-ged","category-numeracy","category-procedural-fluency","category-proportion","category-teaching-conceptually","category-testing","category-visual","tag-estimation","tag-ged","tag-hiset","tag-proportion","tag-ratio","tag-testing"],"acf":[],"cp_meta_data":{"custom_page_title":[""],"_custom_page_title":["field_5db45d9c2601b"],"external_link":[""],"_external_link":["field_5d6033845a92c"],"hide_share_buttons":["1"],"_hide_share_buttons":["field_5e5c1be61306c"],"meta_description":[""],"_meta_description":["field_60dd0445aa562"],"_wp_old_date":["2023-08-29","2025-02-01"],"_relevanssi_related_posts":["1602,1729,1138,2924,2231,2021"],"_relevanssi_pin_keywords":[""],"_relevanssi_unpin_keywords":[""],"footnotes":[""],"_relevanssi_hide_content":["on"],"_relevanssi_pin_for_all":["on"],"_relevanssi_related_keywords":[""],"_relevanssi_related_include_ids":[""],"_relevanssi_related_exclude_ids":[""],"_relevanssi_related_no_append":[""],"_relevanssi_related_not_related":[""],"_dp_original":["3492"],"_edit_last":["16"],"_edit_lock":["1756492509:16"],"_thumbnail_id":["1149"]},"_links":{"self":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts\/3573","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/comments?post=3573"}],"version-history":[{"count":15,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts\/3573\/revisions"}],"predecessor-version":[{"id":3590,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/posts\/3573\/revisions\/3590"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/media\/1149"}],"wp:attachment":[{"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/media?parent=3573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/categories?post=3573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.terc.edu\/adultnumeracycenter\/wp-json\/wp\/v2\/tags?post=3573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}